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Dissertations / Theses on the topic 'Statistical inference'
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1
Thabane, Lehana. "Contributions to Bayesian statistical inference." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq31133.pdf.
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Yang, Liqiang. "Statistical Inference for Gap Data." NCSU, 2000. http://www.lib.ncsu.edu/theses/available/etd-20001110-173900.
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This thesis research is motivated by a special type of missing data - Gap Data, which was first encountered in a cardiology study conducted at Duke Medical School. This type of data include multiple observations of certain event time (in this medical study the event is the reopenning of a certain artery), some of them may have one or more missing periods called ``gaps'' before observing the``first'' event. Therefore, for those observations, the observed first event may not be the true first event because the true first event might have happened in one of the missing gaps. Due to this kind of missing information, estimating the survival function of the true first event becomes very difficult. No research nor discussion has been done on this type of data by now. In this thesis, the auther introduces a new nonparametric estimating method to solve this problem. This new method is currently called Imputed Empirical Estimating (IEE) method. According to the simulation studies, the IEE method provide a very good estimate of the survival function of the true first event. It significantly outperforms all the existing estimating approaches in our simulation studies. Besides the new IEE method, this thesis also explores the Maximum Likelihood Estimate in thegap data case. The gap data is introduced as a special type of interval censored data for thefirst time. The dependence between the censoring interval (in the gap data case is the observedfirst event time point) and the event (in the gap data case is the true first event) makes the gap data different from the well studied regular interval censored data. This thesis points of theonly difference between the gap data and the regular interval censored data, and provides a MLEof the gap data under certain assumptions.The third estimating method discussed in this thesis is the Weighted Estimating Equation (WEE)method. The WEE estimate is a very popular nonparametric approach currently used in many survivalanalysis studies. In this thesis the consistency and asymptotic properties of the WEE estimateused in the gap data are discussed. Finally, in the gap data case, the WEE estimate is showed to be equivalent to the Kaplan-Meier estimate. Numerical examples are provied in this thesis toillustrate the algorithm of the IEE and the MLE approaches. The auther also provides an IEE estimate of the survival function based on the real-life data from Duke Medical School. A series of simulation studies are conducted to assess the goodness-of-fit of the new IEE estimate. Plots and tables of the results of the simulation studies are presentedin the second chapter of this thesis.
3
Sun, Xiaohai. "Causal inference from statistical data /." Berlin : Logos-Verl, 2008. http://d-nb.info/988947331/04.
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Czogiel, Irina. "Statistical inference for molecular shapes." Thesis, University of Nottingham, 2010. http://eprints.nottingham.ac.uk/12217/.
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This thesis is concerned with developing statistical methods for evaluating and comparing molecular shapes. Techniques from statistical shape analysis serve as a basis for our methods. However, as molecules are fuzzy objects of electron clouds which constantly undergo vibrational motions and conformational changes, these techniques should be modified to be more suitable for the distinctive features of molecular shape. The first part of this thesis is concerned with the continuous nature of molecules. Based on molecular properties which have been measured at the atom positions, a continuous field--based representation of a molecule is obtained using methods from spatial statistics. Within the framework of reproducing kernel Hilbert spaces, a similarity index for two molecular shapes is proposed which can then be used for the pairwise alignment of molecules. The alignment is carried out using Markov chain Monte Carlo methods and posterior inference. In the Bayesian setting, it is also possible to introduce additional parameters (mask vectors) which allow for the fact that only part of the molecules may be similar. We apply our methods to a dataset of 31 steroid molecules which fall into three activity classes with respect to the binding activity to a common receptor protein. To investigate which molecular features distinguish the activity classes, we also propose a generalisation of the pairwise method to the simultaneous alignment of several molecules. The second part of this thesis is concerned with the dynamic aspect of molecular shapes. Here, we consider a dataset containing time series of DNA configurations which have been obtained using molecular dynamic simulations. For each considered DNA duplex, both a damaged and an undamaged version are available, and the objective is to investigate whether or not the damage induces a significant difference to the the mean shape of the molecule. To do so, we consider bootstrap hypothesis tests for the equality of mean shapes. In particular, we investigate the use of a computationally inexpensive algorithm which is based on the Procrustes tangent space. Two versions of this algorithm are proposed. The first version is designed for independent configuration matrices while the second version is specifically designed to accommodate temporal dependence of the configurations within each group and is hence more suitable for the DNA data.
5
方以德 and Yee-tak Daniel Fong. "Statistical inference on biomedical models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31210788.
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Liu, Fei, and 劉飛. "Statistical inference for banding data." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B41508701.
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Junklewitz, Henrik. "Statistical inference in radio astronomy." Diss., Ludwig-Maximilians-Universität München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:19-177457.
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This thesis unifies several studies, which all are dedicated to the subject of statistical data
analysis in radio astronomy and radio astrophysics.
Radio astronomy, like astronomy as a whole, has undergone a remarkable development in the past twenty years in introducing new instruments and technologies. New telescopes like the upgraded VLA, LOFAR, or the SKA and its pathfinder missions offer unprecedented sensitivities, previously uncharted frequency domains and unmatched survey capabilities.
Many of these have the potential to significantly advance the science of radio astrophysics and cosmology on all scales, from solar and stellar
physics, Galactic astrophysics and cosmic magnetic fields, to Galaxy cluster astrophysics
and signals from the epoch of reionization.
Since then, radio data analysis, calibration and imaging techniques have entered a similar phase of new development to push the boundaries and adapt the field to the new instruments and scientific opportunities.
This thesis contributes to these greater developments in two specific subjects, radio interferometric imaging and cosmic magnetic field statistics.
Throughout this study, different data analysis techniques are presented and employed
in various settings, but all can be summarized under the broad term of statistical infer-
ence. This subject encompasses a huge variety of statistical techniques, developed to solve
problems in which deductions have to be made from incomplete knowledge, data or measurements. This study focuses especially on Bayesian inference methods that make use of a subjective definition of probabilities, allowing for the expression of probabilities and statistical knowledge prior to an actual measurement.
The thesis contains two different sets of application for such techniques. First, situations
where a complicated, and generally ill-posed measurement problem can be approached by
assuming a statistical signal model prior to infer the desired measured variable. Such
a problem very often is met should the measurement device take less data then needed
to constrain all degrees of freedom of the problem. The principal case investigated in
this thesis is the measurement problem of a radio interferometer, which takes incomplete
samples of the Fourier transformed intensity of the radio emission in the sky, such that it is
impossible to exactly recover the signal. The new imaging algorithm RESOLVE is presented,
optimal for extended radio sources. A first showcase demonstrates the performance of the
new technique on real data. Further, a new Bayesian approach to multi-frequency radio
interferometric imaging is presented and integrated into RESOLVE.
The second field of application are astrophysical problems, in which the inherent stochas-
tic nature of a physical process demands a description, where properties of physical quanti-
ties can only be statistically estimated. Astrophysical plasmas for instance are very often in a turbulent state, and thus governed by statistical hydrodynamical laws. Two studies are presented that show how properties of turbulent plasma magnetic fields can be inferred from radio observations.
8
Bell, Paul W. "Statistical inference for multidimensional scaling." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327197.
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Covarrubias, Carlos Cuevas. "Statistical inference for ROC curves." Thesis, University of Warwick, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.399489.
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Oe, Bianca Madoka Shimizu. "Statistical inference in complex networks." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-28032017-095426/.
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The complex network theory has been extensively used to understand various natural and artificial phenomena made of interconnected parts. This representation enables the study of dynamical processes running on complex systems, such as epidemics and rumor spreading. The evolution of these dynamical processes is influenced by the organization of the network. The size of some real world networks makes it prohibitive to analyse the whole network computationally. Thus it is necessary to represent it by a set of topological measures or to reduce its size by means of sampling. In addition, most networks are samples of a larger networks whose structure may not be captured and thus, need to be inferred from samples. In this work, we study both problems: the influence of the structure of the network in spreading processes and the effects of sampling in the structure of the network. Our results suggest that it is possible to predict the final fraction of infected individuals and the final fraction of individuals that came across a rumor by modeling them with a beta regression model and using topological measures as regressors. The most influential measure in both cases is the average search information, that quantifies the ease or difficulty to navigate through a network. We have also shown that the structure of a sampled network differs from the original network and that the type of change depends on the sampling method. Finally, we apply four sampling methods to study the behaviour of the epidemic threshold of a network when sampled with different sampling rates and found out that the breadth-first search sampling is most appropriate method to estimate the epidemic threshold among the studied ones.Vários fenômenos naturais e artificiais compostos de partes interconectadas vem sendo estudados pela teoria de redes complexas. Tal representação permite o estudo de processos dinâmicos que ocorrem em redes complexas, tais como propagação de epidemias e rumores. A evolução destes processos é influenciada pela organização das conexões da rede. O tamanho das redes do mundo real torna a análise da rede inteira computacionalmente proibitiva. Portanto, torna-se necessário representá-la com medidas topológicas ou amostrá-la para reduzir seu tamanho. Além disso, muitas redes são amostras de redes maiores cuja estrutura é difícil de ser capturada e deve ser inferida de amostras. Neste trabalho, ambos os problemas são estudados: a influência da estrutura da rede em processos de propagação e os efeitos da amostragem na estrutura da rede. Os resultados obtidos sugerem que é possível predizer o tamanho da epidemia ou do rumor com base em um modelo de regressão beta com dispersão variável, usando medidas topológicas como regressores. A medida mais influente em ambas as dinâmicas é a informação de busca média, que quantifica a facilidade com que se navega em uma rede. Também é mostrado que a estrutura de uma rede amostrada difere da original e que o tipo de mudança depende do método de amostragem utilizado. Por fim, quatro métodos de amostragem foram aplicados para estudar o comportamento do limiar epidêmico de uma rede quando amostrada com diferentes taxas de amostragem. Os resultados sugerem que a amostragem por busca em largura é a mais adequada para estimar o limiar epidêmico entre os métodos comparados.
11
ZHAO, SHUHONG. "STATISTICAL INFERENCE ON BINOMIAL PROPORTIONS." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1115834351.
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Liu, Fei. "Statistical inference for banding data." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B41508701.
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Fong, Yee-tak Daniel. "Statistical inference on biomedical models /." [Hong Kong] : University of Hong Kong, 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13456921.
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Peiris, Thelge Buddika. "Constrained Statistical Inference in Regression." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/dissertations/934.
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Regression analysis constitutes a large portion of the statistical repertoire in applications. In case where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem. But in many applications we are interested in a simple parametric model to describe the structure of a system with some prior knowledge of the structure. An important example of this occurs when the experimenter has the strong belief that the regression function changes monotonically in some or all of the predictor variables in a region of interest. The analyses needed for statistical inference under such constraints are nonstandard. The specific aim of this study is to introduce a technique which can be used for statistical inferences of a multivariate simple regression with some non-standard constraints.
15
FANIZZA, MARCO. "Quantum statistical inference and communication." Doctoral thesis, Scuola Normale Superiore, 2021. http://hdl.handle.net/11384/109209.
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This thesis studies the limits on the performances of inference tasks with quantum data
and quantum operations. Our results can be divided in two main parts.
In the first part, we study how to infer relative properties of sets of quantum states,
given a certain amount of copies of the states. We investigate the performance of optimal
inference strategies according to several figures of merit which quantifies the precision of
the inference. Since we are not interested in obtaining a complete reconstruction of the
states, optimal strategies do not require to perform quantum tomography. In particular,
we address the following problems:
- We evaluate the asymptotic error probabilities of optimal learning machines for
quantum state discrimination. Here, a machine receives a number of copies of a
pair of unknown states, which can be seen as training data, together with a test
system which is initialized in one of the states of the pair with equal probability.
The goal is to implement a measurement to discriminate in which state the test
system is, minimizing the error probability. We analyze the optimal strategies for
a number of different settings, differing on the prior incomplete information on the
states available to the agent.
- We evaluate the limits on the precision of the estimation of the overlap between two
unknown pure states, given N and M copies of each state. We find an asymptotic
expansion of a Fisher information associated with the estimation problem, which
gives a lower bound on the mean square error of any estimator. We compute the
minimum average mean square error for random pure states, and we evaluate the
effect of depolarizing noise on qubit states. We compare the performance of the
optimal estimation strategy with the performances of other intuitive strategies,
such as the swap test and measurements based on estimating the states.
- We evaluate how many samples from a collection of N d-dimensional states are
necessary to understand with high probability if the collection is made of identical
states or they differ more than a threshold according to a motivated closeness
measure. The access to copies of the states in the collection is given as follows:
each time the agent ask for a copy of the states, the agent receives one of the states with some fixed probability, together with a different label for each state in the collection. We prove that the problem can be solved with O(pNd=2) copies, and
that this scaling is optimal up to a constant independent on d;N; .
In the second part, we study optimal classical and quantum communication rates for
several physically motivated noise models.
- The quantum and private capacities of most realistic channels cannot be evaluated
from their regularized expressions. We design several degradable extensions
for notable channels, obtaining upper bounds on the quantum and private capacities
of the original channels. We obtain sufficient conditions for the degradability
of flagged extensions of channels which are convex combination of other channels.
These sufficient conditions are easy to verify and simplify the construction of
degradable extensions.
- We consider the problem of transmitting classical information with continuous variable
systems and an energy constraint, when it is impossible to maintain a shared
reference frame and in presence of losses. At variance with phase-insensitive noise
models, we show that, in some regimes, squeezing improves the communication
rates with respect to coherent state sources and with respect to sources producing
up to two-photon Fock states. We give upper and lower bounds on the optimal
coherent state rate and show that using part of the energy to repeatedly restore a
phase reference is strictly suboptimal for high energies.
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Jinn, Nicole Mee-Hyaang. "Toward Error-Statistical Principles of Evidence in Statistical Inference." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/48420.
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The context for this research is statistical inference, the process of making predictions or inferences about a population from observation and analyses of a sample. In this context, many researchers want to grasp what inferences can be made that are valid, in the sense of being able to uphold or justify by argument or evidence. Another pressing question among users of statistical methods is: how can spurious relationships be distinguished from genuine ones? Underlying both of these issues is the concept of evidence. In response to these (and similar) questions, two questions I work on in this essay are: (1) what is a genuine principle of evidence? and (2) do error probabilities have more than a long-run role? Concisely, I propose that felicitous genuine principles of evidence should provide concrete guidelines on precisely how to examine error probabilities, with respect to a test's aptitude for unmasking pertinent errors, which leads to establishing sound interpretations of results from statistical techniques. The starting point for my definition of genuine principles of evidence is Allan Birnbaum's confidence concept, an attempt to control misleading interpretations. However, Birnbaum's confidence concept is inadequate for interpreting statistical evidence, because using only pre-data error probabilities would not pick up on a test's ability to detect a discrepancy of interest (e.g., "even if the discrepancy exists" with respect to the actual outcome. Instead, I argue that Deborah Mayo's severity assessment is the most suitable characterization of evidence based on my definition of genuine principles of evidence.Master of Arts
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Zhai, Yongliang. "Stochastic processes, statistical inference and efficient algorithms for phylogenetic inference." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/59095.
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Phylogenetic inference aims to reconstruct the evolutionary history of populations or species. With the rapid expansion of genetic data available, statistical methods play an increasingly important role in phylogenetic inference by analyzing genetic variation of observed data collected at current populations or species. In this thesis, we develop new evolutionary models, statistical inference methods and efficient algorithms for reconstructing phylogenetic trees at the level of populations using single nucleotide polymorphism data and at the level of species using multiple sequence alignment data. At the level of populations, we introduce a new inference method to estimate evolutionary distances for any two populations to their most recent common ancestral population using single-nucleotide polymorphism allele frequencies. Our method is based on a new evolutionary model for both drift and fixation. To scale this method to large numbers of populations, we introduce the asymmetric neighbor-joining algorithm, an efficient method for reconstructing rooted bifurcating trees. Asymmetric neighbor-joining provides a scalable rooting method applicable to any non-reversible evolutionary modelling setup. We explore the statistical properties of asymmetric neighbor-joining, and demonstrate its accuracy on synthetic data. We validate our method by reconstructing rooted phylogenetic trees from the Human Genome Diversity Panel data. Our results are obtained without using an outgroup, and are consistent with the prevalent recent single-origin model of human migration. At the level of species, we introduce a continuous time stochastic process, the geometric Poisson indel process, that allows indel rates to vary across sites. We design an efficient algorithm for computing the probability of a given multiple sequence alignment based on our new indel model. We describe a method to construct phylogeny estimates from a fixed alignment using neighbor-joining. Using simulation studies, we show that ignoring indel rate variation may have a detrimental effect on the accuracy of the inferred phylogenies, and that our proposed method can sidestep this issue by inferring latent indel rate categories. We also show that our phylogenetic inference method may be more stable to taxa subsampling in a real data experiment compared to some existing methods that either ignore indels or ignore indel rate variation.Science, Faculty of
Statistics, Department of
Graduate
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Gwet, Jean-Philippe. "Robust statistical inference in survey sampling." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22168.pdf.
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Guo, H. "Statistical causal inference and propensity analysis." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599787.
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Statistical causal inference from an observational study often requires adjustment for a possibly multi-dimensional covariate, where there is a need for dimension reduction. Propensity score analysis (Rosenbaum and Rubin 1983) is a popular approach to such reduction. This thesis addresses causal inference within Dawid’s decision-theoretic framework, where studies of “sufficient covariate” and its properties are essential. The role of a propensity variable, obtained from “treatment-sufficient reduction”, is illustrated and examined by a simple normal linear model. As propensity analysis is believed to reduce bias and improve precision, both population-based and sample-based linear regressions have been implemented, with adjustments for the multivariate covariate and for a scalar propensity variable. Theoretical illustrations are then verified by simulation results. In addition, propensity analysis in a non-linear model: logistic regression is also discussed, followed by the investigation of the augmented inverse probability weighted (AIPW) estimator, which is a combination of a response model and a propensity model. It is found that, in the linear regression with homoscedasticity, propensity variable analysis results in exactly the same estimated causal effect as that from multivariate linear regression, for both population and sample. It is claimed that adjusting for an estimated propensity variable yields better precision than the true propensity variable, which is proved to not be universally valid. The AIPW estimator has the property of “Double robustness” and it is possible to improve the precision given that the propensity model is correctly specified.
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屠烈偉 and Lit-wai Tao. "Statistical inference on a mixture model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31977480.
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Mukherjee, Rajarshi. "Statistical Inference for High Dimensional Problems." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11516.
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In this dissertation, we study minimax hypothesis testing in high-dimensional regression against sparse alternatives and minimax estimation of average treatment effect in an semiparametric regression with possibly large number of covariates.
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Nourmohammadi, Mohammad. "Statistical inference with randomized nomination sampling." Elsevier B.V, 2014. http://hdl.handle.net/1993/30150.
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In this dissertation, we develop several new inference procedures that are based on
randomized nomination sampling (RNS). The first problem we consider is that of constructing distribution-free confidence intervals for quantiles for finite populations. The required algorithms for computing coverage probabilities of the proposed confidence intervals are presented. The second problem we address is that of constructing nonparametric confidence
intervals for infinite populations. We describe the procedures for constructing confidence intervals and compare the constructed confidence intervals in the RNS setting, both in perfect and imperfect ranking scenario, with their simple random sampling (SRS) counterparts.
Recommendations for choosing the design parameters are made to achieve shorter confidence intervals than their SRS counterparts. The third problem we investigate is the construction
of tolerance intervals using the RNS technique. We describe the procedures of constructing one- and two-sided RNS tolerance intervals and investigate the sample sizes required to achieve tolerance intervals which contain the determined proportions of the underlying population. We also investigate the efficiency of RNS-based tolerance intervals compared with their corresponding intervals based on SRS. A new method for estimating ranking error
probabilities is proposed. The final problem we consider is that of parametric inference
based on RNS. We introduce different data types associated with different situation that one might encounter using the RNS design and provide the maximum likelihood (ML) and the method of moments (MM) estimators of the parameters in two classes of distributions; proportional hazard rate (PHR) and proportional reverse hazard rate (PRHR) models.
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Thorpe, Matthew. "Variational methods for geometric statistical inference." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/74241/.
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Estimating multiple geometric shapes such as tracks or surfaces creates significant mathematical challenges particularly in the presence of unknown data association. In particular, problems of this type have two major challenges. The first is typically the object of interest is infinite dimensional whilst data is finite dimensional. As a result the inverse problem is ill-posed without regularization. The second is the data association makes the likelihood function highly oscillatory. The focus of this thesis is on techniques to validate approaches to estimating problems in geometric statistical inference. We use convergence of the large data limit as an indicator of robustness of the methodology. One particular advantage of our approach is that we can prove convergence under modest conditions on the data generating process. This allows one to apply the theory where very little is known about the data. This indicates a robustness in applications to real world problems. The results of this thesis therefore concern the asymptotics for a selection of statistical inference problems. We construct our estimates as the minimizer of an appropriate functional and look at what happens in the large data limit. In each case we will show our estimates converge to a minimizer of a limiting functional. In certain cases we also add rates of convergence. The emphasis is on problems which contain a data association or classification component. More precisely we study a generalized version of the k-means method which is suitable for estimating multiple trajectories from unlabeled data which combines data association with spline smoothing. Another problem considered is a graphical approach to estimating the labeling of data points. Our approach uses minimizers of the Ginzburg-Landau functional on a suitably defined graph. In order to study these problems we use variational techniques and in particular I-convergence. This is the natural framework to use for studying sequences of minimization problems. A key advantage of this approach is that it allows us to deal with infinite dimensional and highly oscillatory functionals.
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Chen, Yixin. "Statistical inference for varying coefficient models." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/17690.
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Doctor of PhilosophyDepartment of Statistics
Weixin Yao
This dissertation contains two projects that are related to varying coefficient models. The traditional least squares based kernel estimates of the varying coefficient model will lose some efficiency when the error distribution is not normal. In the first project, we propose a novel adaptive estimation method that can adapt to different error distributions and provide an efficient EM algorithm to implement the proposed estimation. The asymptotic properties of the resulting estimator is established. Both simulation studies and real data examples are used to illustrate the finite sample performance of the new estimation procedure. The numerical results show that the gain of the adaptive procedure over the least squares estimation can be quite substantial for non-Gaussian errors. In the second project, we propose a unified inference for sparse and dense longitudinal data in time-varying coefficient models. The time-varying coefficient model is a special case of the varying coefficient model and is very useful in longitudinal/panel data analysis. A mixed-effects time-varying coefficient model is considered to account for the within subject correlation for longitudinal data. We show that when the kernel smoothing method is used to estimate the smooth functions in the time-varying coefficient model for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases may lead to wrong conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and a real data application.
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Scipione, Catherine Marie. "Statistical inference in nonlinear dynamical systems /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487777170404657.
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Gwet, J. P. (Jean Philippe) Carleton University Dissertation Mathematics and Statistics. "Robust statistical inference in survey sampling." Ottawa, 1997.
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Tao, Lit-wai. "Statistical inference on a mixture model." [Hong Kong] : University of Hong Kong, 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13781479.
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Qin, Yingli. "Statistical inference for high-dimensional data." [Ames, Iowa : Iowa State University], 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3389139.
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Novelli, Marco <1985>. "Statistical Inference in Open Quantum Systems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amsdottorato.unibo.it/7259/1/Novelli_Marco_tesi.pdf.
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This thesis concerns the statistical analysis of open quantum systems subject to an external and non-stationary perturbation.
In the first paper, a generalization of the explicit-duration hidden Markov models (EDHMM) which takes into account the presence of sparse data is presented. Introducing a kernel estimator in the estimation procedure increases the accuracy of the estimates, and thus allows one to obtain a more reliable information about the evolution of the unobservable system.
A generalization of the Viterbi algorithm to EDHMM is developed.
In the second paper, we develop a Markov Chain Monte Carlo (MCMC) procedure for estimating the EDHMM. We improve the flexibility of our formulation by adopting a Bayesian model selection procedure which allows one to avoid a direct specification of the number of states of the hidden chain.
Motivated by the presence of sparsity, we make use of a non-parametric estimator to obtain more accurate estimates of the model parameters. The formulation presented turns out to be straightforward to implement, robust against the underflow problem and provides accurate estimates of the parameters.
In the third paper, an extension of the Cramér-Rao inequality for quantum discrete parameter models is derived. The latter are models in which the parameter space is restricted to a finite set of points.
In some estimation problems indeed, theory provides us with additional information
that allow us to restrict the parameter space to a finite set of points.
The extension presented sets the ultimate accuracy of an estimator, and determines a discrete counterpart of the quantum Fisher information. This is particularly useful in many experiments in which the parameters can assume only few different values: for example, the direction which the magnetic field points to. We also provide an illustration related to a quantum optics problem.
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Novelli, Marco <1985>. "Statistical Inference in Open Quantum Systems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amsdottorato.unibo.it/7259/.
Full textAbstract:
This thesis concerns the statistical analysis of open quantum systems subject to an external and non-stationary perturbation.
In the first paper, a generalization of the explicit-duration hidden Markov models (EDHMM) which takes into account the presence of sparse data is presented. Introducing a kernel estimator in the estimation procedure increases the accuracy of the estimates, and thus allows one to obtain a more reliable information about the evolution of the unobservable system.
A generalization of the Viterbi algorithm to EDHMM is developed.
In the second paper, we develop a Markov Chain Monte Carlo (MCMC) procedure for estimating the EDHMM. We improve the flexibility of our formulation by adopting a Bayesian model selection procedure which allows one to avoid a direct specification of the number of states of the hidden chain.
Motivated by the presence of sparsity, we make use of a non-parametric estimator to obtain more accurate estimates of the model parameters. The formulation presented turns out to be straightforward to implement, robust against the underflow problem and provides accurate estimates of the parameters.
In the third paper, an extension of the Cramér-Rao inequality for quantum discrete parameter models is derived. The latter are models in which the parameter space is restricted to a finite set of points.
In some estimation problems indeed, theory provides us with additional information
that allow us to restrict the parameter space to a finite set of points.
The extension presented sets the ultimate accuracy of an estimator, and determines a discrete counterpart of the quantum Fisher information. This is particularly useful in many experiments in which the parameters can assume only few different values: for example, the direction which the magnetic field points to. We also provide an illustration related to a quantum optics problem.
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Pasetto, Michela Eugenia <1989>. "Statistical Inference for the Duffing Process." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amsdottorato.unibo.it/8514/1/Pasetto.pdf.
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The aim of the research concerns inference methods for non-linear dynamical systems. In particular, the focus is on a differential equation called Duffing oscillator. This equation is suitable to model non-linear phenomena like jumps, hysteresis, or subharmonics and it may lead to chaotic behaviour as control parameters vary. Such behaviour have been observed in many different real-world scenarios, as in economics or biology.
Inference in the Duffing process is performed with the unscented Kalman filter (UKF) by casting the system in state space form. In the context of ordinary differential equations, the uncertainty of the UKF estimates for chaotic systems is quantified by a simulation study. To overcome the limitations of the UKF when applied to the Duffing process, a new algorithm that matches Bayesian optimization (BO) and approximate Bayesian computation (ABC) within the UKF scheme is proposed. The novelty consists in (i) optimizing the sigma points location by means of maximization of the likelihood of observations with BO, and (ii) initialize the UKF with candidate parameters coming from the ABC scheme. The proposed algorithm can outperform the UKF in complex systems where the likelihood function is highly multi-modal.
Concerning stochastic differential equations, a massive simulation study is presented to evaluate the performance of the UKF for parameter estimation.
Finally, illustrations of the method with real data and further developments of the research are discussed.La presente ricerca ha l'obiettivo di sviluppare metodi d'inferenza per sistemi dinamici non lineari. In particolare, l'analisi è incentrata su una equazione differenziale chiamata l'oscillatore di Duffing. Tale equazione è utilizzata per modellare diversi fenomeni non lineari, quali salti, isteresi o subarmoniche, e, in generale, può mostrare comportamenti caotici al variare di parametri di controllo. Tali fenomeni sono diffusi in diversi scenari reali, sia in economia sia in biologia. L'inferenza nel processo di Duffing è condotta tramite unscented Kalman filter (UKF) attraverso la riscrittura del sistema nella forma stato-spazio. Nel contesto di equazioni differenziali ordinarie, l'incertezza delle stime di UKF per sistemi caotici è quantificato tramite uno studio di simulazione. Per superare le limitazioni di UKF quando applicato al sistema di Duffing, viene proposto un nuovo algoritmo che unisce ottimizzazione bayesiana (BO) e approximate bayesian computation (ABC) all'interno dello schema UKF. Le novità del metodo consistono in: (i) ottimizzazione della posizione dei punti sigma tramite la massimizzazione della verosimiglianza delle osservazioni e (ii) inizializzazione di UKF con valori provenienti dallo schema ABC. L'algoritmo proposto può portare stime dei parametri migliori rispetto a UKF nel caso di sistemi complessi dove la funzione di verosimiglianza è altamente multi-modale. Per l'analisi di equazioni differenziali stocastiche, viene presentato un cospicuo studio di simulazione al fine di valutare i risultati del UKF per la stima dei parametri. Infine, si illustra un'applicazione del metodo su dati reali e si discutono gli sviluppi futuri della ricerca.
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Frey, Jesse C. "Inference procedures based on order statistics." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1122565389.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains xi, 148 p.; also includes graphics. Includes bibliographical references (p. 146-148). Available online via OhioLINK's ETD Center
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El, Ghouch Anouar. "Nonparametric statistical inference for dependent censored data." Université catholique de Louvain, 2007. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-09262007-123927/.
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A frequent problem that appears in practical survival data analysis is censoring. A censored observation occurs when the observation of the event time (duration or survival time) may be prevented by the occurrence of an earlier competing event (censoring time). Censoring may be due to different causes. For example, the loss of some subjects under study, the end of the follow-up period, drop out or the termination of the study and the limitation in the sensitivity of a measurement instrument. The literature about censored data focuses on the i.i.d. case. However in many real applications the data are collected sequentially in time or space and so the assumption of independence in such case does not hold. Here we only give some typical examples from the literature involving correlated data which are subject to censoring. In the clinical trials domain it frequently happens that the patients from the same hospital have correlated survival times due to unmeasured variables like the quality of the hospital equipment. Censored correlated data are also a common problem in the domain of environmental and spatial (geographical or ecological) statistics. In fact, due to the process being used in the data sampling procedure, e.g. the analytical equipment, only the measurements which exceed some thresholds, for example the method detection limits or the instrumental detection limits, can be included in the data analysis. Many other examples can also be found in other fields like econometrics and financial statistics. Observations on duration of unemployment e.g., may be right censored and are typically correlated. When the data are not independent and are subject to censoring, estimation and inference become more challenging mathematical problems with a wide area of applications. In this context, we propose here some new and flexible tools based on a nonparametric approach. More precisely, allowing dependence between individuals, our main contribution to this domain concerns the following aspects. First, we are interested in developing more suitable confidence intervals for a general class of functionals of a survival distribution via the empirical likelihood method. Secondly, we study the problem of conditional mean estimation using the local linear technique. Thirdly, we develop and study a new estimator of the conditional quantile function also based on the local linear method. In this dissertation, for each proposed method, asymptotic results like consistency and asymptotic normality are derived and the finite sample performance is evaluated in a simulation study.
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Can, Mutan Oya. "Statistical Inference From Complete And Incomplete Data." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12611531/index.pdf.
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Let X and Y be two random variables such that Y depends on X=x. This is a very common situation in many real life applications. The problem is to estimate the location and scale parameters in the marginal distributions of X and Y and the conditional distribution of Y given X=x. We are also interested in estimating the regression coefficient and the correlation coefficient. We have a cost constraint for observing X=x, the larger x is the more expensive it becomes. The allowable sample size n is governed by a pre-determined total cost. This can lead to a situation where some of the largest X=x observations cannot be observed (Type II censoring). Two general methods of estimation are available, the method of least squares and the method of maximum likelihood. For most non-normal distributions, however, the latter is analytically and computationally problematic. Instead, we use the method of modified maximum likelihood estimation which is known to be essentially as efficient as the maximum likelihood estimation. The method has a distinct advantage: It yields estimators which are explicit functions of sample observations and are, therefore, analytically and computationally straightforward. In this thesis specifically, the problem is to evaluate the effect of the largest order statistics x(i) (i>n-r) in a random sample of size n (i) on the mean E(X) and variance V(X) of X, (ii) on the cost of observing the x-observations, (iii) on the conditional mean E(Y|X=x) and variance V(Y|X=x) and (iv) on the regression coefficient. It is shown that unduly large x-observations have a detrimental effect on the allowable sample size and the estimators, both least squares and modified maximum likelihood. The advantage of not observing a few largest observations are evaluated. The distributions considered are Weibull, Generalized Logistic and the scaled Student&rsquo
s t.
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Ng, Edmund Tze-Man. "Statistical inference for heterogeneous event history data." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22223.pdf.
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Eklund, Bruno. "Four contributions to statistical inference in econometrics." Doctoral thesis, Stockholm : Economic Research Institute, Stockholm School of Economics [Ekonomiska forskningsinstitutet vid Handelshögsk.] (EFI), 2003. http://www.hhs.se/efi/summary/624.htm.
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Källberg, David. "Nonparametric Statistical Inference for Entropy-type Functionals." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-79976.
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In this thesis, we study statistical inference for entropy, divergence, and related functionals of one or two probability distributions. Asymptotic properties of particular nonparametric estimators of such functionals are investigated. We consider estimation from both independent and dependent observations. The thesis consists of an introductory survey of the subject and some related theory and four papers (A-D). In Paper A, we consider a general class of entropy-type functionals which includes, for example, integer order Rényi entropy and certain Bregman divergences. We propose U-statistic estimators of these functionals based on the coincident or epsilon-close vector observations in the corresponding independent and identically distributed samples. We prove some asymptotic properties of the estimators such as consistency and asymptotic normality. Applications of the obtained results related to entropy maximizing distributions, stochastic databases, and image matching are discussed. In Paper B, we provide some important generalizations of the results for continuous distributions in Paper A. The consistency of the estimators is obtained under weaker density assumptions. Moreover, we introduce a class of functionals of quadratic order, including both entropy and divergence, and prove normal limit results for the corresponding estimators which are valid even for densities of low smoothness. The asymptotic properties of a divergence-based two-sample test are also derived. In Paper C, we consider estimation of the quadratic Rényi entropy and some related functionals for the marginal distribution of a stationary m-dependent sequence. We investigate asymptotic properties of the U-statistic estimators for these functionals introduced in Papers A and B when they are based on a sample from such a sequence. We prove consistency, asymptotic normality, and Poisson convergence under mild assumptions for the stationary m-dependent sequence. Applications of the results to time-series databases and entropy-based testing for dependent samples are discussed. In Paper D, we further develop the approach for estimation of quadratic functionals with m-dependent observations introduced in Paper C. We consider quadratic functionals for one or two distributions. The consistency and rate of convergence of the corresponding U-statistic estimators are obtained under weak conditions on the stationary m-dependent sequences. Additionally, we propose estimators based on incomplete U-statistics and show their consistency properties under more general assumptions.
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Yuan, Yinyin. "Statistical inference from large-scale genomic data." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/1066/.
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This thesis explores the potential of statistical inference methodologies in their applications in functional genomics. In essence, it summarises algorithmic findings in this field, providing step-by-step analytical methodologies for deciphering biological knowledge from large-scale genomic data, mainly microarray gene expression time series. This thesis covers a range of topics in the investigation of complex multivariate genomic data. One focus involves using clustering as a method of inference and another is cluster validation to extract meaningful biological information from the data. Information gained from the application of these various techniques can then be used conjointly in the elucidation of gene regulatory networks, the ultimate goal of this type of analysis. First, a new tight clustering method for gene expression data is proposed to obtain tighter and potentially more informative gene clusters. Next, to fully utilise biological knowledge in clustering validation, a validity index is defined based on one of the most important ontologies within the Bioinformatics community, Gene Ontology. The method bridges a gap in current literature, in the sense that it takes into account not only the variations of Gene Ontology categories in biological specificities and their significance to the gene clusters, but also the complex structure of the Gene Ontology. Finally, Bayesian probability is applied to making inference from heterogeneous genomic data, integrated with previous efforts in this thesis, for the aim of large-scale gene network inference. The proposed system comes with a stochastic process to achieve robustness to noise, yet remains efficient enough for large-scale analysis. Ultimately, the solutions presented in this thesis serve as building blocks of an intelligent system for interpreting large-scale genomic data and understanding the functional organisation of the genome.
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曾達誠 and Tat-shing Tsang. "Statistical inference on the coefficient of variation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31223503.
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Golalizadeh, Lehi Mousa. "Statistical modelling and inference for shape diffusions." Thesis, University of Nottingham, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435446.
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Cecchini, Gloria. "Improving network inference by overcoming statistical limitations." Thesis, University of Aberdeen, 2019. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=240835.
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A reliable inference of networks from data is of key interest in many scientific fields. Several methods have been suggested in the literature to reliably determine links in a network. These techniques rely on statistical methods, typically controlling the number of false positive links, but not considering false negative links. In this thesis new methodologies to improve network inference are suggested. Initial analyses demonstrate the impact of false positive and false negative conclusions about the presence or absence of links on the resulting inferred network. Consequently, revealing the importance of making well-considered choices leads to suggest new approaches to enhance existing network reconstruction methods. A simulation study, presented in Chapter 3, shows that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. The existence of type I and type II errors in the reconstructed network, also called biased network, is accepted. Consequently, an analytic method that describes the influence of these two errors on the network structure is explored. As a result of this analysis, an analytic formula of the density of the biased vertex degree distribution is found (Chapter 4). In the inverse problem, the vertex degree distribution of the true underlying network is analytically reconstructed, assuming the probabilities of type I and type II errors. Chapters 4-5 show that the method is robust to incorrect estimates of α and β within reasonable limits. In Chapter 6, an iterative procedure to enhance this method is presented in the case of large errors on the estimates of α and β. The investigations presented so far focus on the influence of false positive and false negative links on the network characteristics. In Chapter 7, the analysis is reversed - the study focuses on the influence of network characteristics on the probability of type I and type II errors, in the case of networks of coupled oscillators. The probabilities of α and β are influenced by the shortest path length and the detour degree, respectively. These results have been used to improve the network reconstruction, when the true underlying network is not known a priori, introducing a novel and advanced concept of threshold.
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Almarashi, Abdullah Maedh. "Statistical inference for Poisson time series models." Thesis, University of Strathclyde, 2014. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=23669.
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There are many nonlinear econometric models which are useful in analysis of financial time series. In this thesis, we consider two kinds of nonlinear autoregressive models for nonnegative integer-valued time series: threshold autoregressive models and Markov switching models, in which the conditional distribution given historical information is the Poisson distribution. The link between the conditional variance (i.e. the conditional mean for the Poisson distribution) and its past values as well as the observed values of the Poisson process may be different according to the threshold variable in threshold autoregressive models, and to an unobservable state variable in Markov switching models in different regimes. We give a condition on parameters under which the Poisson generalized threshold autoregressive heteroscedastic (PTGARCH) process can be approximated by a geometrically ergodic process. Under this condition, we discuss statistical inference (estimation and tests) for PTGARCH models, and give the asymptotic theory on the inference. The complete structure of the threshold autoregressive model is not exactly specific in economic theory for the most financial applications of the model. In particular, the number of regimes, the value of threshold and the delay parameter are often unknown and cannot be assumed known. Therefore, in this research, the performance of various information criteria for choosing the number of regimes, the threshold value and the delay parameters for different sample sizes is investigated. Tests for threshold nonlinearity are applied. The characteristics of Markovian switching Poisson generalized autoregressive hetero-scedastic (MS-PGARCH) models are given, and the maximum likelihood estimation of parameters is discussed. Simulation studies and applications to modelling financial counting time series are presented to support our methodology for both the PTGARCH model and the MS-PGARCH model.
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Salimi-Khorshidi, Gholamreza. "Statistical models for neuroimaging meta-analytic inference." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:40a10327-7f36-42e7-8120-ae04bd8be1d4.
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A statistical meta-analysis combines the results of several studies that address a set of related research hypotheses, thus increasing the power and reliability of the inference. Meta-analytic methods are over 50 years old and play an important role in science; pooling evidence from many trials to provide answers that any one trial would have insufficient samples to address. On the other hand, the number of neuroimaging studies is growing dramatically, with many of these publications containing conflicting results, or being based on only a small number of subjects. Hence there has been increasing interest in using meta-analysis methods to find consistent results for a specific functional task, or for predicting the results of a study that has not been performed directly. Current state of neuroimaging meta-analysis is limited to coordinate-based meta-analysis (CBMA), i.e., using only the coordinates of activation peaks that are reported by a group of studies, in order to "localize" the brain regions that respond to a certain type of stimulus. This class of meta-analysis suffers from a series of problems and hence cannot result in as accurate results as desired. In this research, we describe the problems that existing CBMA methods are suffering from and introduce a hierarchical mixed-effects image-based metaanalysis (IBMA) solution that incorporates the sufficient statistics (i.e., voxel-wise effect size and its associated uncertainty) from each study. In order to improve the statistical-inference stage of our proposed IBMA method, we introduce a nonparametric technique that is capable of adjusting such an inference for spatial nonstationarity. Given that in common practice, neuroimaging studies rarely provide the full image data, in an attempt to improve the existing CBMA techniques we introduce a fully automatic model-based approach that employs Gaussian-process regression (GPR) for estimating the meta-analytic statistic image from its corresponding sparse and noisy observations (i.e., the collected foci). To conclude, we introduce a new way to approach neuroimaging meta-analysis that enables the analysis to result in information such as “functional connectivity” and networks of the brain regions’ interactions, rather than just localizing the functions.
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Cerqueira, Andressa. "Statistical inference on random graphs and networks." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-04042018-094802/.
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In this thesis we study two probabilistic models defined on graphs: the Stochastic Block model and the Exponential Random Graph. Therefore, this thesis is divided in two parts. In the first part, we introduce the Krichevsky-Trofimov estimator for the number of communities in the Stochastic Block Model and prove its eventual almost sure convergence to the underlying number of communities, without assuming a known upper bound on that quantity. In the second part of this thesis we address the perfect simulation problem for the Exponential random graph model. We propose an algorithm based on the Coupling From The Past algorithm using a Glauber dynamics. This algorithm is efficient in the case of monotone models. We prove that this is the case for a subset of the parametric space. We also propose an algorithm based on the Backward and Forward algorithm that can be applied for monotone and non monotone models. We prove the existence of an upper bound for the expected running time of both algorithms.Nessa tese estudamos dois modelos probabilísticos definidos em grafos: o modelo estocástico por blocos e o modelo de grafos exponenciais. Dessa forma, essa tese está dividida em duas partes. Na primeira parte nós propomos um estimador penalizado baseado na mistura de Krichevsky-Trofimov para o número de comunidades do modelo estocástico por blocos e provamos sua convergência quase certa sem considerar um limitante conhecido para o número de comunidades. Na segunda parte dessa tese nós abordamos o problema de simulação perfeita para o modelo de grafos aleatórios Exponenciais. Nós propomos um algoritmo de simulação perfeita baseado no algoritmo Coupling From the Past usando a dinâmica de Glauber. Esse algoritmo é eficiente apenas no caso em que o modelo é monotóno e nós provamos que esse é o caso para um subconjunto do espaço paramétrico. Nós também propomos um algoritmo de simulação perfeita baseado no algoritmo Backward and Forward que pode ser aplicado à modelos monótonos e não monótonos. Nós provamos a existência de um limitante superior para o número esperado de passos de ambos os algoritmos.
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Csilléry, Katalin. "Statistical inference in population genetics using microsatellites." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/3865.
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Statistical inference from molecular population genetic data is currently a very active area of research for two main reasons. First, in the past two decades an enormous amount of molecular genetic data have been produced and the amount of data is expected to grow even more in the future. Second, drawing inferences about complex population genetics problems, for example understanding the demographic and genetic factors that shaped modern populations, poses a serious statistical challenge. Amongst the many different kinds of genetic data that have appeared in the past two decades, the highly polymorphic microsatellites have played an important role. Microsatellites revolutionized the population genetics of natural populations, and were the initial tool for linkage mapping in humans and other model organisms. Despite their important role, and extensive use, the evolutionary dynamics of microsatellites are still not fully understood, and their statistical methods are often underdeveloped and do not adequately model microsatellite evolution. In this thesis, I address some aspects of this problem by assessing the performance of existing statistical tools, and developing some new ones. My work encompasses a range of statistical methods from simple hypothesis testing to more recent, complex computational statistical tools. This thesis consists of four main topics. First, I review the statistical methods that have been developed for microsatellites in population genetics applications. I review the different models of the microsatellite mutation process, and ask which models are the most supported by data, and how models were incorporated into statistical methods. I also present estimates of mutation parameters for several species based on published data. Second, I evaluate the performance of estimators of genetic relatedness using real data from five vertebrate populations. I demonstrate that the overall performance of marker-based pairwise relatedness estimators mainly depends on the population relatedness composition and may only be improved by the marker data quality within the limits of the population relatedness composition. Third, I investigate the different null hypotheses that may be used to test for independence between loci. Using simulations I show that testing for statistical independence (i.e. zero linkage disequilibrium, LD) is difficult to interpret in most cases, and instead a null hypothesis should be tested, which accounts for the “background LD” due to finite population size. I investigate the utility of a novel approximate testing procedure to circumvent this problem, and illustrate its use on a real data set from red deer. Fourth, I explore the utility of Approximate Bayesian Computation, inference based on summary statistics, to estimate demographic parameters from admixed populations. Assuming a simple demographic model, I show that the choice of summary statistics greatly influences the quality of the estimation, and that different parameters are better estimated with different summary statistics. Most importantly, I show how the estimation of most admixture parameters can be considerably improved via the use of linkage disequilibrium statistics from microsatellite data.
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Liu, Ge. "Statistical Inference for Multivariate Stochastic Differential Equations." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1562966204796479.
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Liu, Shibo. "Statistical inference and efficient portfolio investment performance." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15185.
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Two main methods have been used in mutual funds evaluation. One is portfolio evaluation, and the other is data envelopment analysis (DEA). The history of portfolio evaluation dates from the 1960s with emphasis on both expected return and risk. However, there are many criticisms of traditional portfolio analysis which focus on their sensitivity to chosen benchmarks. Imperfections in portfolio analysis models have led to the exploration of other methodologies to evaluate fund performance, in particular data envelopment analysis (DEA). DEA is a non-parametric methodology for measuring relative performance based on mathematical programming. Based on the unique characteristics of investment trusts, Morey and Morey (1999) developed a mutual funds efficiency measure in a traditional mean-variance model. It was based on Markowitz portfolio theory and related the non-parametric methodologies to the foundations of traditional performance measurement in mean-variance space. The first application in this thesis is to apply the non-linear programming calculation of the efficient frontier in mean variance space outlined in Morey and Morey (1999) to a new modern data set comprising a multi-year sample of investment funds. One limitation of DEA is the absence of sampling error from the methodology. Therefore the second innovation in this thesis extends Morey and Morey (1999) model by the application of bootstrapped probability density functions in order to develop confidence intervals for the relative performance indicators. This has not previously been achieved for the DEA frontier in mean variance space so that the DEA efficiency scores obtained through Morey and Morey (1999) model have not hitherto been tested for statistical significance. The third application in this thesis is to examine the efficiency of investment trusts in order to analyze the factors contributing to investment trusts' performance and detect the determinants of inefficiency. Robust-OLS regression, Tobit models and Papke-Wooldridge (PW) models are conducted and compared to evaluate contextual variables affecting the performance of investment funds. From the thesis, new and original Matlab codes designed for Morey and Morey (1999) models are presented. With the Matlab codes, not only the results are obtained, but also how this quadratic model is programming could be very clearly seen, with all the details revealed.
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Tsang, Tat-shing. "Statistical inference on the coefficient of variation /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B21903980.
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Wozny, David R. "Statistical inference in multisensory perception and learning." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1970597951&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Zhou, Ziqian. "Statistical inference of distributed delay differential equations." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2173.
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In this study, we aim to develop new likelihood based method for estimating parameters of ordinary differential equations (ODEs) / delay differential equations (DDEs) models. Those models are important for modeling dynamical processes that are described in terms of their derivatives and are widely used in many fields of modern science, such as physics, chemistry, biology and social sciences. We use our new approach to study a distributed delay differential equation model, the statistical inference of which has been unexplored, to our knowledge. Estimating a distributed DDE model or ODE model with time varying coefficients results in a large number of parameters. We also apply regularization for efficient estimation of such models. We assess the performance of our new approaches using simulation and applied them to analyzing data from epidemiology and ecology.