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1
Li, Lingzhu. "Model checking for general parametric regression models." HKBU Institutional Repository, 2019. https://repository.hkbu.edu.hk/etd_oa/654.
Full textAbstract:
Model checking for regressions has drawn considerable attention in the last three decades. Compared with global smoothing tests, local smoothing tests, which are more sensitive to high-frequency alternatives, can only detect local alternatives dis- tinct from the null model at a much slower rate when the dimension of predictor is high. When the number of covariates is large, nonparametric estimations used in local smoothing tests lack efficiency. Corresponding tests then have trouble in maintaining the significance level and detecting the alternatives. To tackle the issue, we propose two methods under high but fixed dimension framework. Further, we investigate a model checking test under divergent dimension, where the numbers of covariates and unknown parameters go divergent with the sample size n. The first proposed test is constructed upon a typical kernel-based local smoothing test using projection method. Employed by projection and integral, the resulted test statistic has a closed form that depends only on the residuals and distances of the sample points. A merit of the developed test is that the distance is easy to implement compared with the kernel estimation, especially when the dimension is high. Moreover, the test inherits some feature of local smoothing tests owing to its construction. Although it is eventually similar to an Integrated Conditional Moment test in spirit, it leads to a test with a weight function that helps to collect more information from the samples than Integrated Conditional Moment test. Simulations and real data analysis justify the powerfulness of the test. The second test, which is a synthesis of local and global smoothing tests, aims at solving the slow convergence rate caused by nonparametric estimation in local smoothing tests. A significant feature of this approach is that it allows nonparamet- ric estimation-based tests, under the alternatives, also share the merits of existing empirical process-based tests. The proposed hybrid test can detect local alternatives at the fastest possible rate like the empirical process-based ones, and simultane- ously, retains the sensitivity to high-frequency alternatives from the nonparametric estimation-based ones. This feature is achieved by utilizing an indicative dimension in the field of dimension reduction. As a by-product, we have a systematic study on a residual-related central subspace for model adaptation, showing when alterna- tive models can be indicated and when cannot. Numerical studies are conducted to verify its application. Since the data volume nowadays is increasing, the numbers of predictors and un- known parameters are probably divergent as sample size n goes to infinity. Model checking under divergent dimension, however, is almost uncharted in the literature. In this thesis, an adaptive-to-model test is proposed to handle the divergent dimen- sion based on the two previous introduced tests. Theoretical results tell that, to get the asymptotic normality of the parameter estimator, the number of unknown parameters should be in the order of o(n1/3). Also, as a spinoff, we demonstrate the asymptotic properties of estimations for the residual-related central subspace and central mean subspace under different hypotheses.
2
Lo, Sau Yee. "Measurement error in logistic regression model /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20LO.
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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004.<br>Includes bibliographical references (leaves 82-83). Also available in electronic version. Access restricted to campus users.
3
Gandy, Axel. "Directed model checks for regression models from survival analysis." Berlin Logos-Ver, 2005. http://deposit.ddb.de/cgi-bin/dokserv?id=2766731&prov=M&dok_var=1&dok_ext=htm.
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Gandy, Axel. "Directed model checks for regression models from survival analysis /." Berlin : Logos-Ver, 2006. http://deposit.ddb.de/cgi-bin/dokserv?id=2766731&prov=M&dok_var=1&dok_ext=htm.
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Ranganai, Edmore. "Aspects of model development using regression quantiles and elemental regressions." Thesis, Stellenbosch : Stellenbosch University, 2007. http://hdl.handle.net/10019.1/18668.
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Dissertation (PhD)--University of Stellenbosch, 2007.<br>ENGLISH ABSTRACT: It is well known that ordinary least squares (OLS) procedures are sensitive to deviations from
the classical Gaussian assumptions (outliers) as well as data aberrations in the design space.
The two major data aberrations in the design space are collinearity and high leverage.
Leverage points can also induce or hide collinearity in the design space. Such leverage points
are referred to as collinearity influential points. As a consequence, over the years, many
diagnostic tools to detect these anomalies as well as alternative procedures to counter them
were developed. To counter deviations from the classical Gaussian assumptions many robust
procedures have been proposed. One such class of procedures is the Koenker and Bassett
(1978) Regressions Quantiles (RQs), which are natural extensions of order statistics, to the
linear model. RQs can be found as solutions to linear programming problems (LPs). The basic
optimal solutions to these LPs (which are RQs) correspond to elemental subset (ES)
regressions, which consist of subsets of minimum size to estimate the necessary parameters of
the model.
On the one hand, some ESs correspond to RQs. On the other hand, in the literature it is shown
that many OLS statistics (estimators) are related to ES regression statistics (estimators).
Therefore there is an inherent relationship amongst the three sets of procedures. The
relationship between the ES procedure and the RQ one, has been noted almost “casually” in
the literature while the latter has been fairly widely explored. Using these existing
relationships between the ES procedure and the OLS one as well as new ones, collinearity,
leverage and outlier problems in the RQ scenario were investigated. Also, a lasso procedure
was proposed as variable selection technique in the RQ scenario and some tentative results
were given for it. These results are promising.
Single case diagnostics were considered as well as their relationships to multiple case ones. In
particular, multiple cases of the minimum size to estimate the necessary parameters of the
model, were considered, corresponding to a RQ (ES). In this way regression diagnostics were
developed for both ESs and RQs. The main problems that affect RQs adversely are
collinearity and leverage due to the nature of the computational procedures and the fact that
RQs’ influence functions are unbounded in the design space but bounded in the response
variable. As a consequence of this, RQs have a high affinity for leverage points and a high
exclusion rate of outliers. The influential picture exhibited in the presence of both leverage points and outliers is the net result of these two antagonistic forces. Although RQs are
bounded in the response variable (and therefore fairly robust to outliers), outlier diagnostics
were also considered in order to have a more holistic picture.
The investigations used comprised analytic means as well as simulation. Furthermore,
applications were made to artificial computer generated data sets as well as standard data sets
from the literature. These revealed that the ES based statistics can be used to address
problems arising in the RQ scenario to some degree of success. However, due to the
interdependence between the different aspects, viz. the one between leverage and collinearity
and the one between leverage and outliers, “solutions” are often dependent on the particular
situation. In spite of this complexity, the research did produce some fairly general guidelines
that can be fruitfully used in practice.<br>AFRIKAANSE OPSOMMING: Dit is bekend dat die gewone kleinste kwadraat (KK) prosedures sensitief is vir afwykings
vanaf die klassieke Gaussiese aannames (uitskieters) asook vir data afwykings in die
ontwerpruimte. Twee tipes afwykings van belang in laasgenoemde geval, is kollinearitiet en
punte met hoë hefboom waarde. Laasgenoemde punte kan ook kollineariteit induseer of
versteek in die ontwerp. Na sodanige punte word verwys as kollinêre hefboom punte. Oor die
jare is baie diagnostiese hulpmiddels ontwikkel om hierdie afwykings te identifiseer en om
alternatiewe prosedures daarteen te ontwikkel. Om afwykings vanaf die Gaussiese aanname
teen te werk, is heelwat robuuste prosedures ontwikkel. Een sodanige klas van prosedures is
die Koenker en Bassett (1978) Regressie Kwantiele (RKe), wat natuurlike uitbreidings is van
rangorde statistieke na die lineêre model. RKe kan bepaal word as oplossings van lineêre
programmeringsprobleme (LPs). Die basiese optimale oplossings van hierdie LPs (wat RKe
is) kom ooreen met die elementale deelversameling (ED) regressies, wat bestaan uit
deelversamelings van minimum grootte waarmee die parameters van die model beraam kan
word.
Enersyds geld dat sekere EDs ooreenkom met RKe. Andersyds, uit die literatuur is dit bekend
dat baie KK statistieke (beramers) verwant is aan ED regressie statistieke (beramers). Dit
impliseer dat daar dus ‘n inherente verwantskap is tussen die drie klasse van prosedures. Die
verwantskap tussen die ED en die ooreenkomstige RK prosedures is redelik “terloops” van
melding gemaak in die literatuur, terwyl laasgenoemde prosedures redelik breedvoerig
ondersoek is. Deur gebruik te maak van bestaande verwantskappe tussen ED en KK
prosedures, sowel as nuwes wat ontwikkel is, is kollineariteit, punte met hoë hefboom
waardes en uitskieter probleme in die RK omgewing ondersoek. Voorts is ‘n lasso prosedure
as veranderlike seleksie tegniek voorgestel in die RK situasie en is enkele tentatiewe resultate
daarvoor gegee. Hierdie resultate blyk belowend te wees, veral ook vir verdere navorsing.
Enkel geval diagnostiese tegnieke is beskou sowel as hul verwantskap met meervoudige geval
tegnieke. In die besonder is veral meervoudige gevalle beskou wat van minimum grootte is
om die parameters van die model te kan beraam, en wat ooreenkom met ‘n RK (ED). Met
sodanige benadering is regressie diagnostiese tegnieke ontwikkel vir beide EDs en RKe. Die
belangrikste probleme wat RKe negatief beinvloed, is kollineariteit en punte met hoë
hefboom waardes agv die aard van die berekeningsprosedures en die feit dat RKe se invloedfunksies begrensd is in die ruimte van die afhanklike veranderlike, maar onbegrensd is
in die ontwerpruimte. Gevolglik het RKe ‘n hoë affiniteit vir punte met hoë hefboom waardes
en poog gewoonlik om uitskieters uit te sluit. Die finale uitset wat verkry word wanneer beide
punte met hoë hefboom waardes en uitskieters voorkom, is dan die netto resultaat van hierdie
twee teenstrydige pogings. Alhoewel RKe begrensd is in die onafhanklike veranderlike (en
dus redelik robuust is tov uitskieters), is uitskieter diagnostiese tegnieke ook beskou om ‘n
meer holistiese beeld te verkry.
Die ondersoek het analitiese sowel as simulasie tegnieke gebruik. Voorts is ook gebruik
gemaak van kunsmatige datastelle en standard datastelle uit die literatuur. Hierdie ondersoeke
het getoon dat die ED gebaseerde statistieke met ‘n redelike mate van sukses gebruik kan
word om probleme in die RK omgewing aan te spreek. Dit is egter belangrik om daarop te let
dat as gevolg van die interafhanklikheid tussen kollineariteit en punte met hoë hefboom
waardes asook dié tussen punte met hoë hefboom waardes en uitskieters, “oplossings”
dikwels afhanklik is van die bepaalde situasie. Ten spyte van hierdie kompleksiteit, is op
grond van die navorsing wat gedoen is, tog redelike algemene riglyne verkry wat nuttig in die
praktyk gebruik kan word.
6
Tan, Falong. "Projected adaptive-to-model tests for regression models." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/390.
Full textAbstract:
This thesis investigates Goodness-of-Fit tests for parametric regression models. With the help of sufficient dimension reduction techniques, we develop adaptive-to-model tests using projection in both the fixed dimension settings and the diverging dimension settings. The first part of the thesis develops a globally smoothing test in the fixed dimension settings for a parametric single index model. When the dimension p of covariates is larger than 1, existing empirical process-based tests either have non-tractable limiting null distributions or are not omnibus. To attack this problem, we propose a projected adaptive-to-model approach. If the null hypothesis is a parametric single index model, our method can fully utilize the dimension reduction structure under the null as if the regressors were one-dimensional. Then a martingale transformation proposed by Stute, Thies, and Zhu (1998) leads our test to be asymptotically distribution-free. Moreover, our test can automatically adapt to the underlying alternative models such that it can be omnibus and thus detect all alternative models departing from the null at the fastest possible convergence rate in hypothesis testing. A comparative simulation is conducted to check the performance of our test. We also apply our test to a self-noise mechanisms data set for illustration. The second part of the thesis proposes a globally smoothing test for parametric single-index models in the diverging dimension settings. In high dimensional data analysis, the dimension p of covariates is often large even though it may be still small compared with the sample size n. Thus we should regard p as a diverging number as n goes to infinity. With this in mind, we develop an adaptive-to-model empirical process as the basis of our test statistic, when the dimension p of covariates diverges to infinity as the sample size n tends to infinity. We also show that the martingale transformation proposed by Stute, Thies, and Zhu (1998) still work in the diverging dimension settings. The limiting distributions of the adaptive-to-model empirical process under both the null and the alternative are discussed in this new situation. Simulation examples are conducted to show the performance of this test when p grows with the sample size n. The last Chapter of the thesis considers the same problem as in the second part. Bierens's (1982) first constructed tests based on projection pursuit techniques and obtained an integrated conditional moment (ICM) test. We notice that Bierens's (1982) test performs very badly for large p, although it may be viewed as a globally smoothing test. With the help of sufficient dimension techniques, we propose an adaptive-to-model integrated conditional moment test for regression models in the diverging dimension setting. We also give the asymptotic properties of the new tests under both the null and alternative hypotheses in this new situation. When p grows with the sample size n, simulation studies show that our new tests perform much better than Bierens's (1982) original test.
7
Volinsky, Christopher T. "Bayesian model averaging for censored survival models /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/8944.
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8
Liu, Hai. "Semiparametric regression analysis of zero-inflated data." Diss., University of Iowa, 2009. https://ir.uiowa.edu/etd/308.
Full textAbstract:
Zero-inflated data abound in ecological studies as well as in other scientific and quantitative fields. Nonparametric regression with zero-inflated response may be studied via the zero-inflated generalized additive model (ZIGAM). ZIGAM assumes that the conditional distribution of the response variable belongs to the zero-inflated 1-parameter exponential family which is a probabilistic mixture of the zero atom and the 1-parameter exponential family, where the zero atom accounts for an excess of zeroes in the data. We propose the constrained zero-inflated generalized additive model (COZIGAM) for analyzing zero-inflated data, with the further assumption that the probability of non-zero-inflation is some monotone function of the (non-zero-inflated) exponential family distribution mean. When the latter assumption obtains, the new approach provides a unified framework for modeling zero-inflated data, which is more parsimonious and efficient than the unconstrained ZIGAM. We develop an iterative algorithm for model estimation based on the penalized likelihood approach, and derive formulas for constructing confidence intervals of the maximum penalized likelihood estimator. Some asymptotic properties including the consistency of the regression function estimator and the limiting distribution of the parametric estimator are derived. We also propose a Bayesian model selection criterion for choosing between the unconstrained and the constrained ZIGAMs. We consider several useful extensions of the COZIGAM, including imposing additive-component-specific proportional and partial constraints, and incorporating threshold effects to account for regime shift phenomena. The new methods are illustrated with both simulated data and real applications. An R package COZIGAM has been developed for model fitting and model selection with zero-inflated data.
9
Roualdes, Edward A. "New Results in ell_1 Penalized Regression." UKnowledge, 2015. http://uknowledge.uky.edu/statistics_etds/13.
Full textAbstract:
Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate the variation of estimates – a notoriously difficult task for the frequentist formulation. We then introduce Bayesian trend filtering which exemplifies the benefits of our Bayesian version. Bayesian trend filtering is shown to be an empirically strong technique for fitting univariate, nonparametric regression. Through a simulation study, we show that Bayesian trend filtering reduces prediction error and attains more accurate coverage probabilities over the frequentist method. We then apply Bayesian trend filtering to real data sets, where our method is quite competitive against a number of other popular nonparametric methods.
10
Bunea, Florentina. "A model selection approach to partially linear regression /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/8971.
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Ryu, Duchwan. "Regression analysis with longitudinal measurements." Texas A&M University, 2005. http://hdl.handle.net/1969.1/2398.
Full textAbstract:
Bayesian approaches to the regression analysis for longitudinal measurements are
considered. The history of measurements from a subject may convey characteristics
of the subject. Hence, in a regression analysis with longitudinal measurements, the
characteristics of each subject can be served as covariates, in addition to possible other
covariates. Also, the longitudinal measurements may lead to complicated covariance
structures within each subject and they should be modeled properly.
When covariates are some unobservable characteristics of each subject, Bayesian
parametric and nonparametric regressions have been considered. Although covariates
are not observable directly, by virtue of longitudinal measurements, the covariates
can be estimated. In this case, the measurement error problem is inevitable. Hence,
a classical measurement error model is established. In the Bayesian framework, the
regression function as well as all the unobservable covariates and nuisance parameters
are estimated. As multiple covariates are involved, a generalized additive model is
adopted, and the Bayesian backfitting algorithm is utilized for each component of the
additive model. For the binary response, the logistic regression has been proposed,
where the link function is estimated by the Bayesian parametric and nonparametric
regressions. For the link function, introduction of latent variables make the computing
fast.
In the next part, each subject is assumed to be observed not at the prespecifiedtime-points. Furthermore, the time of next measurement from a subject is supposed to
be dependent on the previous measurement history of the subject. For this outcome-
dependent follow-up times, various modeling options and the associated analyses
have been examined to investigate how outcome-dependent follow-up times affect
the estimation, within the frameworks of Bayesian parametric and nonparametric
regressions. Correlation structures of outcomes are based on different correlation
coefficients for different subjects. First, by assuming a Poisson process for the follow-
up times, regression models have been constructed. To interpret the subject-specific
random effects, more flexible models are considered by introducing a latent variable
for the subject-specific random effect and a survival distribution for the follow-up
times. The performance of each model has been evaluated by utilizing Bayesian
model assessments.
12
Al-Shaikh, Enas. "Longitudinal Regression Analysis Using Varying Coefficient Mixed Effect Model." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1342543464.
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Mu, He Qing. "Bayesian model class selection on regression problems." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2492988.
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Zhu, Xuehu. "Model-adaptive tests for regressions." HKBU Institutional Repository, 2015. https://repository.hkbu.edu.hk/etd_oa/189.
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In this thesis, we firstly develop a model-adaptive checking method for partially parametric single-index models, which combines the advantages of both dimension reduction technique and global smoothing tests. Besides, we propose a dimension reduction-based model adaptive test of heteroscedasticity checks for nonparametric and semi-parametric regression models. Finally, to extend our testing approaches to nonparametric regressions with some restrictions, we consider significance testing under a nonparametric framework. In Chapter 2, “Model Checking for Partially Parametric Single-index Models: A Model-adaptive Approach", we consider the model checking problems for more general parametric models which include generalized linear models and generalized nonlinear models. We develop a model-adaptive dimension reduction test procedure by extending an existing directional test. Compared with traditional smoothing model checking methodologies, the procedure of this test not only avoids the curse of dimensionality but also is an omnibus test. The resulting test is omnibus adapting the null and alternative models to fully utilize the dimension-reduction structure under the null hypothesis and can detect fully nonparametric global alternatives, and local alternatives distinct from the null model at a convergence rate as close to square root of the sample size as possible. Finally, both Monte Carlo simulation studies and real data analysis are conducted to compare with existing tests and illustrate the finite sample performance of the new test. In Chapter 3,Heteroscedasticity Checks for Nonparametric and Semi-parametric Regression Model: A Dimension Reduction Approach", we consider heteroscedasticity checks for nonparametric and semi-parametric regression models. Existing local smoothing tests suffer severely from the curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In this chapter, we propose a dimension reduction-based model adaptive test that behaves like a local smoothing test as if the number of covariates is equal to the number of their linear combinations in the mean regression function, in particular, equal to 1 when the mean function contains a single index. The test statistic is asymptotically normal under the null hypothesis such that critical values are easily determined. The finite sample performances of the test are examined by simulations and a real data analysis. In Chapter 4，Dimension Reduction-based Significance Testing in Nonparametric Regression", as nonparametric techniques need much less restrictive conditions than those required for parametric approaches, we consider to check nonparametric regressions with some restrictions under sufficient dimension reduction structure. A dimension-reduction-based model-adaptive test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a local smoothing test as if the number of covariates is just that under the null hypothesis and it can detect local alternative hypotheses distinct from the null hypothesis at the rate that is only related to the number of covariates under the null hypothesis. Thus, the curse of dimensionality is largely alleviated when nonparametric estimation is inevitably required. In the cases where there are many insignificant covariates, the improvement of the new test is very significant over existing local smoothing tests on the significance level maintenance and power enhancement. Simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed test. Finally, we conclude the main results and discuss future research directions in Chapter 5. Keywords: Model checking; Partially parametric single-index models; Central mean subspace; Central subspace; Partial central subspace; Dimension reduction; Ridge-type eigenvalue ratio estimate; Model-adaption; Heteroscedasticity checks; Significance testing.
15
Heise, Mark A. "Optimal designs for a bivariate logistic regression model." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/38538.
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In drug-testing experiments the primary responses of interest are efficacy and toxicity. These can be modeled as a bivariate quantal response using the Gumbel model for bivariate logistic regression. D-optimal and Q-optimal experimental designs are developed for this model The Q-optimal design minimizes the average asymptotic prediction variance of p(l,O;d), the probability of efficacy without toxicity at dose d, over a desired range of doses. In addition, a new optimality criterion, T -optimality, is developed which minimizes the asymptotic variance of the estimate of the therapeutic index.
Most experimenters will be less familiar with the Gumbel bivariate logistic regression model than with the univariate logistic regression models which comprise its marginals. Therefore, the optimal designs based on the Gumbel model are evaluated based on univariate logistic regression D-efficiencies; conversely, designs derived from the univariate logistic regression model are evaluated with respect to the Gumbel optimality criteria.
Further practical considerations motivate an exploration of designs providing a maximum compromise between the three Gumbel-based criteria D, Q and T. Finally, 5-point designs which can be generated by fitted equations are proposed as a practical option for experimental use.<br>Ph. D.
16
Neugebauer, Shawn Patrick. "Robust Analysis of M-Estimators of Nonlinear Models." Thesis, Virginia Tech, 1996. http://hdl.handle.net/10919/36557.
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Estimation of nonlinear models finds applications in every field of engineering and the sciences. Much work has been done to build solid statistical theories for its use and interpretation. However, there has been little analysis of the tolerance of nonlinear model estimators to deviations from assumptions and normality.
We focus on analyzing the robustness properties of M-estimators of nonlinear models by studying the effects of deviations from assumptions and normality on these estimators. We discuss St. Laurent and Cook's Jacobian Leverage and identify the relationship of the technique to the robustness concept of influence. We derive influence functions for M-estimators of nonlinear models and show that influence of position becomes, more generally, influence of model. The result shows that, for M-estimators, we must bound not only influence of residual but also influence of model. Several examples highlight the unique problems of nonlinear model estimation and demonstrate the utility of the influence function.<br>Master of Science
17
Lee, Wai Hong. "Variable selection for high dimensional transformation model." HKBU Institutional Repository, 2010. http://repository.hkbu.edu.hk/etd_ra/1161.
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Sasieni, Peter D. "Beyond the Cox model : extensions of the model and alternative estimators /." Thesis, Connect to this title online; UW restricted, 1989. http://hdl.handle.net/1773/9556.
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Ni, Xuelei. "New results in detection, estimation, and model selection." Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-12042005-190654/.
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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006.<br>Xiaoming Huo, Committee Chair ; C. F. Jeff Wu, Committee Member ; Brani Vidakovic, Committee Member ; Liang Peng, Committee Member ; Ming Yuan, Committee Member.
20
Chang, Ziqing. "On single-index model and its related topics." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1075.
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Sutherland, Sindee S. "Sequential design augmentation with model misspecification." Diss., This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-10032007-171611/.
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Stark, J. Alex. "Statistical model selection techniques for data analysis." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390190.
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Pan, Tianshu. "Using the multivariate multilevel logistic regression model to detect DIF a comparison with HGLM and logistic regression DIF detection methods /." Diss., Connect to online resource - MSU authorized users, 2008.
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Thesis (PH. D.)--Michigan State University. Measurement and Quantitative Methods, 2008.<br>Title from PDF t.p. (viewed on Sept. 8, 2009) Includes bibliographical references (p. 85-89). Also issued in print.
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Chen, Baixi. "Gaussian Process Regression-Based Data-Driven Material Models for Stochastic Structural Analysis." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/28827.
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The data-driven material models have attracted many researchers recently, as they could directly use material data. However, there are limited studies about material uncertainty in previous data-driven models. This thesis proposes a new Gaussian Process Regression (GPR)-based approach to capture the material behaviour and the associated material uncertainty from the dataset.
The GPR approach is firstly used for the nonlinear elastic behaviour. The obtained GPR-based model is verified by the material datasets. Then, an improved GPR model, called the Heteroscedastic Sparse Gaussian Process Regression (HSGPR) model, is applied for the plastic flow behaviour. The flow stress predicted by the HSGPR model also agrees with the experiments. As a new data-driven material model is introduced, the associated frameworks, which implement the GPR-based model and HSGPR-based model into the finite element method for structural reliability analysis, are developed. The frame problem is used to demonstrate the GPR-based model in the elastic stochastic structural analysis, while the beam and punch problems validate the HSGPR-based model in the plastic stochastic structural analysis. It is concluded that the GPR-based approach can accurately identify both the elastic and plastic stochastic structural responses.
To consider the possible correlation of the stochastic material behaviours, a novel GPR-based approach, which combines the HSGPR model with the Proper Orthogonal Decomposition (POD) algorithm, is proposed. Two case studies on the metal strength and the rock joint behaviour have demonstrated that the material behaviours correlation can be effectively retained in the POD-HSGPR-based model. As indicated by its application in a rock slope problem, it is critical to consider the material properties correlation for the accurate evaluation of structural reliability.
25
Zhang, Ying. "Symbolic Regression of Thermo-Physical Model Using Genetic Programming." Scholar Commons, 2004. https://scholarcommons.usf.edu/etd/1316.
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The symbolic regression problem is to find a function, in symbolic form, that fits a given data set. Symbolic regression provides a means for function identification. This research describes an adaptive hybrid system for symbolic function identification of thermo-physical model that combines the genetic programming and a modified Marquardt nonlinear regression algorithm.
Genetic Programming (GP) system can extract knowledge from the data in the form of symbolic expressions, i.e. a tree structure, that are used to model and derive equation of state, mixing rules and phase behavior from the experimental data (properties estimation).
During the automatic evolution process of GP, the function structure of generated individual module could be highly complicated. To ensure the convergence of the regression, a modified Marquardt regression algorithm is used. Two stop criteria are attached to the traditional Marquardt algorithm to enforce the algorithm repeat the regression process before it stops.
Statistic analysis is applied to the fitted model. Residual plot is used to test the goodness of fit. The χ2-test is used to test the model's adequacy.
Ten experiments are run with different form of input variables, number of data points, standard errors added to data set, and fitness functions. The results show that the system is able to find models and optimize for its parameters successfully.
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Wesso, Gilbert R. "The econometrics of structural change: statistical analysis and forecasting in the context of the South African economy." University of the Western Cape, 1994. http://hdl.handle.net/11394/7907.
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Philosophiae Doctor - PhD<br>One of the assumptions of conventional regression analysis is I that the parameters are constant over all observations. It has often been suggested that this may not be a valid assumption to make, particularly if the econometric model is to be used for economic forecasting0 Apart from this it is also found that econometric models, in particular, are used to investigate the underlying interrelationships of the system under consideration in order to understand and to explain relevant phenomena in structural analysis. The pre-requisite of such use of
econometrics is that the regression parameters of the model is assumed to be constant over time or across different crosssectional
units.
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Xie, Chuanlong. "Model checking for regressions when variables are measured with errors." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/445.
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In this thesis, we investigate model checking problems for parametric single-index regression models when the variables are measured with different types of errors. The large sample behaviours of the test statistics can be used to develop properly centered and scaled model checking procedures. In addition, a dimension reduction model-adaptive strategy is employed, with the special requirements for the models with measurement errors, to improve the proposed testing procedures. This makes the test statistics converge to their weak limit under the null hypothesis with the convergence rates not depending on the dimension of predictor vector. Furthermore, the proposed tests behave like a classical local smoothing test with only one-dimensional predictor. Therefore the proposed methods have potential for alleviating the difficulties associated with high dimensionality in hypothesis testing.. Chapter 2 provides some tests for a parametric single-index regression model when predictors are measured with errors in an additive manner and validation dataset is available. The two proposed tests have consistency rates not depending on the dimension of predictor vector. One of these tests has a bias term that may become arbitrarily large with increasing sample size, but has smaller asymptotic variance. The other test is asymptotically unbiased with larger asymptotic variance. Both are still omnibus against general alternatives. Besides, a systematic study is conducted to give an insight on the effect of the ratio between the size of primary data and the size of validation data on the asymptotic behavior of these tests. Simulation studies are carried out to examine the finite-sample performances of the proposed tests. Also the tests are applied to a real data set about breast cancer with validation data obtained from a nutrition study.. Chapter 3 introduces a minimum projected-distance test for a parametric single-index regression model when predictors are measured with Berkson type errors. The distribution of the measurement error is assumed to be known up to several parameters. This test is constructed by combining the minimum distance test with a dimension reduction model-adaptive strategy. After properly centering, the minimum projected-distance test statistic is asymptotically normal at a convergence rate of order nh^(1/2) and can detect a sequence of local alternatives distinct from the null model with a rate of order n^(-1/2) h^(-1/4) where n is the sample size and h is a sequence of bandwidths tending to 0 as n tends infinity. These rates do not depend on the dimensionality of predictor vector, which implies that the proposed test has potential for alleviating the curse of dimensionality in hypothesis testing in this field. Further, as the test is asymptotically biased, two bias-correction methods are suggested to construct asymptotically unbiased tests. In addition, we discuss some details in the implementation of the proposed tests and then provide a simplified procedure. Simulations indicate desirable finite-sample performances of the tests. Besides, we illustrate the proposed model checking procedures by using two real datasets to illustrate the effects of air pollution on Emphysema.. Chapter 4 provides a nonparametric test for checking a parametric single-index regression model when predictor vector and response are measured with distortion errors. We estimate the true values of response and predictor, and then plug the estimated values into a test statistic to develop a model checking procedure. The dimension reduction model-adaptive strategy is also employed to improve its theoretical properties and finite sample performance. Another interesting observation in this work is that, with properly selected bandwidths and kernel functions in a limited range, the proposed test statistic has the same limiting distribution as that under the classical regression setup without distortion measurement errors. Simulation studies are conducted.
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Kinns, David Jonathan. "Multiple case influence analysis with particular reference to the linear model." Thesis, University of Birmingham, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368427.
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Hayles, Kelly, and kellyhayles@iinet net au. "A Property Valuation Model for Rural Victoria." RMIT University. Mathematical and Geospatial Sciences, 2006. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20070221.150256.
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Licensed valuers in the State of Victoria, Australia currently appraise rural land using manual techniques. Manual techniques typically involve site visits to the property, liaison with property owners through interview, and require a valuer experienced in agricultural properties to determine a value. The use of manual techniques typically takes longer to determine a property value than for valuations performed using automated techniques, providing appropriate data are available. Manual methods of valuation can be subjective and lead to bias in valuation estimates, especially where valuers have varying levels of experience within a specific regional area. Automation may lend itself to more accurate valuation estimates by providing greater consistency between valuations. Automated techniques presently in use for valuation include artificial neural networks, expert systems, case based reasoning and multiple regression analysis. The latter technique appears mo st widely used for valuation. The research aimed to develop a conceptual rural property valuation model, and to develop and evaluate quantitative models for rural property valuation based on the variables identified in the conceptual model. The conceptual model was developed by examining peer research, Valuation Best Practice Standards, a standard in use throughout Victoria for rating valuations, and rural property valuation texts. Using data that are only available digitally and publicly, the research assessed this conceptualisation using properties from four LGAs in the Wellington and Wimmera Catchment Management Authority (CMAs) areas in Victoria. Cluster analysis was undertaken to assess if the use of sub-markets, that are determined statistically, can lead to models that are more accurate than sub-markets that have been determined using geographically defined areas. The research is divided into two phases; the 'available data phase' and the 'restricted data phase'. The 'available data phase' used publicly available digital data to build quantitative models to estimate the value of rural properties. The 'restricted data phase' used data that became available near the completion of the research. The research examined the effect of using statistically derived sub-markets as opposed to geographically derived ones for property valuation. Cluster analysis was used during both phases of model development and showed that one of the clusters developed in the available data phase was superior in its model prediction compared to the models produced using geographically derived regions. A number of limitations with the digital property data available for Victoria were found. Although GIS analysis can enable more property characteristics to be derived and measured from existing data, it is reliant on having access to suitable digital data. The research also identified limitations with the metadata elements in use in Victoria (ANZMETA DTD version 1). It is hypothesised that to further refine the models and achieve greater levels of price estimation, additional properties would need to be sourced and added to the current property database. It is suggested that additional research needs to address issues associated with sub-market identification. If results of additional modelling indicated significantly different levels of price estimation, then these models could be used with manual techniques to evaluate manually derived valuation estimates.
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Zhang, Dongmin. "Open source software maturity model based on linear regression and Bayesian analysis." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1454.
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MATYATIM, Rosliza. "The Classification Model for Corporate Failures in Malaysia." Graduate School of International Development, Nagoya University, 2006. http://hdl.handle.net/2237/7314.
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Diodati-Nolin, Anna C. "Predicting the power of an intraocular lens implant : an application of model selection theory." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63338.
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Chen, Jinbo. "Semiparametric efficient and inefficient estimation for the auxiliary outcome problem with the conditional mean model /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/9531.
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Yeasmin, Mahbuba 1965. "Multiple maxima of likelihood functions and their implications for inference in the general linear regression model." Monash University, Dept. of Econometrics and Business Statistics, 2003. http://arrow.monash.edu.au/hdl/1959.1/5821.
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Leodolter, Johannes. "A Statistical Analysis of the Lake Levels at Lake Neusiedl." Austrian Statistical Society, 2008. http://epub.wu.ac.at/5634/1/296%2D1009%2D1%2DSM.pdf.
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A long record of daily data is used to study the lake levels of Lake Neusiedl, a large steppe lake at the eastern border of Austria. Daily lake level changes are modeled as functions of precipitation, temperature, and wind conditions. The occurrence and the amount of daily precipitation
are modeled with logistic regressions and generalized linear models.
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Jinnah, Ali. "Inference for Cox's regression model via a new version of empirical likelihood." unrestricted, 2007. http://etd.gsu.edu/theses/available/etd-11272007-223933/.
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Thesis (M.S.)--Georgia State University, 2007.<br>Title from file title page. Yichuan Zhao, committee chair; Yu-Sheng Hsu , Xu Zhang, Yuanhui Xiao , committee members. Electronic text (54 p.) : digital, PDF file. Description based on contents viewed Feb. 25, 2008. Includes bibliographical references (p. 30-32).
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SILVA, José Wesley Lima. "Modelagem da biomassa e da quantidade de carbono de clones de Eucalyptus da Chapada do Araripe-PE." Universidade Federal Rural de Pernambuco, 2016. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/4565.
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Previous issue date: 2016-02-25<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The objective of this study was to quantify and test different regression models to estimate
the biomass and the amount of carbon from the aerial parts of Eucalyptus clones planted in the Northeastern semi-arid region, and select the best equations based on R2 aj, the Akaike information criterion (AIC), Furnival Index (FI), the graphical analysis of the residuals and through the Shapiro-Wilk, Breusch- Pagan and Durbin Watson tests. The database came from an experiment with 15 Eucalyptus spp. clones conducted at the Experimental Station of the Agricultural Research Institute of Pernambuco – IPA, located in the municipality of Araripina - PE. Through a completely random sampling process 75 trees were selected, in which were determined the fresh weight and leaf samples collected were samples of leaf, branch, bark and bole to determine the average wood density, biomass and carbon content. The most productive clone in terms of biomass and carbon was the hybrid E. urophylla natural crossing. The average plant biomass accumulation was 59.64 t h−1 and the amount of carbon 24.96 t h−1. The adjustment of the regression models showed that each partition presented particular behavior of dry biomass production and total carbon. It was not possible to select a common model that represents all of parts of the trees. For the variable biomass, the models of Schumacher and Hall, Spurr, the logistics and the exponential model 11 presented the best fits. For the amount of organic carbon the models 6 and exponential 11 presented best results.<br>O objetivo deste trabalho foi quantificar e testar diferentes modelos de regressão, para estimar a biomassa e a quantidade de carbono das partes aéreas de clones de Eucalyptus plantados na região semiárida nordestina, e selecionar as melhores equações com base no R2 aj, nos critérios de informação de Akaike (AIC), no Índice de Furnival (IF), pela análise gráfica dos resíduos e por meio dos testes de Shapiro-Wilk, Breusch-Pagan e Durbin-Watson. A base de dados foi proveniente de um experimento com 15 clones de
Eucalyptus spp. realizado na Estação Experimental da Empresa Pernambucana de Pesquisa Agropecuária – IPA, localizado no município de Araripina – PE. Por meio do processo de amostragem inteiramente aleatória foram cubadas 75 árvores, nas quais se determinaram os pesos frescos, bem como foram coletadas amostras de folhas, galhos, casca e fuste para determinação da densidade média da madeira, biomassa e teor de carbono. O clone mais produtivo em termo de biomassa e carbono foi o híbrido de E. urophylla cruzamento natural. O acúmulo de biomassa médio da plantação foi de 59,64 t h−1 e da quantidade de
carbono 24,96 t h h−1. No ajuste dos modelos de regressão, verificou-se que cada partição apresentou comportamento particular de produção de biomassa seca, carbono total, não sendo possível selecionar um modelo comum que representasse todas elas. Para a variável biomassa o os modelos de Shumarcher e Hall, de Spurr, o logístico e o exponencial modelo 11 foram os que melhor se ajustaram. Para a quantidade de carbono orgânico o modelo 6 e o exponencial 11 se ajustaram a maior parte dos componentes aéreos.
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Laird, Daniel T. "Analysis of Covariance with Linear Regression Error Model on Antenna Control Unit Tracking." International Foundation for Telemetering, 2015. http://hdl.handle.net/10150/596393.
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ITC/USA 2015 Conference Proceedings / The Fifty-First Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2015 / Bally's Hotel & Convention Center, Las Vegas, NV<br>Over the past several years DoD imposed constraints on test deliverables, requiring objective measures of test results, i.e., statistically defensible test and evaluation (SDT&E) methods and results. These constraints force the tester to employ statistical hypotheses, analyses and perhaps modeling to assess test results objectively, i.e., based on statistical metrics, probability of confidence and logical inference to supplement rather than rely solely on expertise, which is too subjective. Experts often disagree on interpretation. Numbers, although interpretable, are less variable than opinion. Logic, statistical inference and belief are the bases of testable, repeatable and refutable hypothesis and analyses. In this paper we apply linear regression modeling and analysis of variance (ANOVA) to time-space position information (TSPI) to determine if a telemetry (TM) antenna control unit (ACU) under test (AUT) tracks statistically, thus as efficiently, in C-band while receiving both C- and S-band signals. Together, regression and ANOVA compose a method known as analysis of covariance (ANCOVA). In this, the second of three papers, we use data from a range test, but make no reference to the systems under test, nor to causes of error. The intent is to present examples of tools and techniques useful for SDT&E methodologies in testing.
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Ni, Xuelei. "New results in detection, estimation, and model selection." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/10419.
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This thesis contains two parts: the detectability of convex sets and the study on regression models
In the first part of this dissertation, we investigate the problem of the detectability of an inhomogeneous convex region in a Gaussian random field. The first proposed detection method relies on checking a constructed statistic on each convex set within an nn image, which is proven to be un-applicable. We then consider using h(v)-parallelograms as the surrogate, which leads to a multiscale strategy. We prove that 2/9 is the minimum proportion of the maximally embedded h(v)-parallelogram in a convex set. Such a constant indicates the effectiveness of the above mentioned multiscale detection method.
In the second part, we study the robustness, the optimality, and the computing for regression models. Firstly, for robustness, M-estimators in a regression model where the residuals are of unknown but stochastically bounded distribution are analyzed. An asymptotic minimax M-estimator (RSBN) is derived. Simulations demonstrate the robustness and advantages. Secondly, for optimality, the analysis on the least angle regressions inspired us to consider the conditions under which a vector is the solution of two optimization problems. For these two problems, one can be solved by certain stepwise algorithms, the other is the objective function in many existing subset selection criteria (including Cp, AIC, BIC, MDL, RIC, etc). The latter is proven to be NP-hard. Several conditions are derived. They tell us when a vector is the common optimizer. At last, extending the above idea about finding conditions into exhaustive subset selection in regression, we improve the widely used leaps-and-bounds algorithm (Furnival and Wilson). The proposed method further reduces the number of subsets needed to be considered in the exhaustive subset search by considering not only the residuals, but also the model matrix, and the current coefficients.
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Pavlik, Kaylin. "A Model to Predict Matriculation of Concordia College Applicants." Thesis, North Dakota State University, 2017. https://hdl.handle.net/10365/28463.
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Colleges and universities are under mounting pressure to meet enrollment goals in the face of declining college attendance. Insight into student-level probability of enrollment, as well as the identification of features relevant in student enrollment decisions, would assist in the allocation of marketing and recruitment resources and the development of future yield programs. A logistic regression model was fit to predict which applicants will ultimately matriculate (enroll) at Concordia College. Demographic, geodemographic and behavioral features were used to build a logistic regression model to assign probability of enrollment to each applicant. Behaviors indicating interest (campus visits, submitting a deposit) and residing in a zip code with high alumni density were found to be strong predictors of matriculation. The model was fit to minimize false negative rate, which was limited to 18.1 percent, compared to 50-60 percent reported by comparable studies. Overall, the model was 80.13 percent accurate.
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Lee, Michelle Oi San. "Sample size calculation for testing an interaction effect in a logistic regression under measurement error model /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20LEE.
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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.<br>Includes bibliographical references (leaves 66-67). Also available in electronic version. Access restricted to campus users.
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Tan, Chunwei Jeffrey. "A model for predicting the repair costs of U.S. Navy inventory items." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2003. http://library.nps.navy.mil/uhtbin/hyperion-image/03Dec%5FTan%5FC.pdf.
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Thesis (M.S. in Operations Research)--Naval Postgraduate School, December 2003.<br>Thesis advisor(s): Robert A. Koyak, Lyn R. Whitaker. Includes bibliographical references (p. 63). Also available online.
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Izadi, Hooshang. "Censored regression and the Pearson system of distributions : an estimation method and application to demand analysis." Thesis, University of Essex, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252929.
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clements, john s. III. "Agricultural Commodity Futures and Farmland Investment: A Regional Analysis." Digital Archive @ GSU, 2010. http://digitalarchive.gsu.edu/real_estate_diss/8.
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Using seventeen years of data from 1991 to 2008, I derive a pricing model for farmland values. This valuation model is the first using agricultural commodity futures as a proxy for “ex ante” income projections for the crops grown or livestock grazed on United States farmland. While not all inclusive, the model is tested regionally including the Corn Belt, Delta States, Lake States, Mountain, Pacific Northwest, Pacific West and Southeast Regions. Additionally, I test whether interest rate futures contracts have a relationship with farmland values as interest rates have been proven to be a reliable predictor in past research. Farmland capitalization rates and anticipated inflation have hypothesized relationships, but are mainly used as control variables in the study.
In general, agricultural commodity futures contracts are a poor predictor of changes in farmland market values. When examining relationships with quarterly percentage change regression models of the included variables, I find the Mountain region provides the most reliable pricing model where both live cattle and Minnesota wheat futures contracts has a positive statistically significant relationships with farmland market values. Also, wheat futures prices have a significant relationship with farmland values in the Corn Belt region. Interest rate futures contracts, farmland capitalization rates and anticipated inflation are not statistically significant in the majority of the regions.
As a robustness check, I model the price levels of the variables using Johansen’s cointegration procedure. This time-series econometric methodology provides results in regards to long-run equilibrium relationships between the variables. The results are only slightly better. Corn, orange juice and sugar futures contracts have positive statistically significant relationships with farmland market values in multiple regions. Again, wheat has a statistically significant positive relationship with farmland values in the Corn Belt region. The Mountain region and interest rate futures contracts are not applicable for the cointegration tests as they are not integrated to the order of one.
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Lee, Kyeong Eun. "Bayesian models for DNA microarray data analysis." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/2465.
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Selection of signi?cant genes via expression patterns is important in a microarray problem. Owing to small sample size and large number of variables (genes), the selection process can be unstable. This research proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables in a regression setting and use a Bayesian mixture prior to perform the variable selection. Due to the binary nature of the data, the posterior distributions of the parameters are not in explicit form, and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the posterior distributions. The Bayesian model is ?exible enough to identify the signi?cant genes as well as to perform future predictions. The method is applied to cancer classi?cation via cDNA microarrays. In particular, the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify the set of signi?cant genes to classify BRCA1 and others. Microarray data can also be applied to survival models. We address the issue of how to reduce the dimension in building model by selecting signi?cant genes as well as assessing the estimated survival curves. Additionally, we consider the wellknown Weibull regression and semiparametric proportional hazards (PH) models for survival analysis. With microarray data, we need to consider the case where the number of covariates p exceeds the number of samples n. Speci?cally, for a given vector of response values, which are times to event (death or censored times) and p gene expressions (covariates), we address the issue of how to reduce the dimension by selecting the responsible genes, which are controlling the survival time. This approach enables us to estimate the survival curve when n << p. In our approach, rather than ?xing the number of selected genes, we will assign a prior distribution to this number. The approach creates additional ?exibility by allowing the imposition of constraints, such as bounding the dimension via a prior, which in e?ect works as a penalty. To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method. We demonstrate the use of the methodology with (a) di?use large B??cell lymphoma (DLBCL) complementary DNA (cDNA) data and (b) Breast Carcinoma data. Lastly, we propose a mixture of Dirichlet process models using discrete wavelet transform for a curve clustering. In order to characterize these time??course gene expresssions, we consider them as trajectory functions of time and gene??speci?c parameters and obtain their wavelet coe?cients by a discrete wavelet transform. We then build cluster curves using a mixture of Dirichlet process priors.
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Chen, Cuixian. "Asymptotic properties of the Buckley-James estimator for a bivariate interval censorship regression model." Diss., Online access via UMI:, 2007.
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Wang, Guoshen. "Analysis of Additive Risk Model with High Dimensional Covariates Using Correlation Principal Component Regression." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/51.
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One problem of interest is to relate genes to survival outcomes of patients for the purpose of building regression models to predict future patients¡¯ survival based on their gene expression data. Applying semeparametric additive risk model of survival analysis, this thesis proposes a new approach to conduct the analysis of gene expression data with the focus on model¡¯s predictive ability. The method modifies the correlation principal component regression to handle the censoring problem of survival data. Also, we employ the time dependent AUC and RMSEP to assess how well the model predicts the survival time. Furthermore, the proposed method is able to identify significant genes which are related to the disease. Finally, this proposed approach is illustrated by simulation data set, the diffuse large B-cell lymphoma (DLBCL) data set, and breast cancer data set. The results show that the model fits both of the data sets very well.
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VACCARELLA, SALVATORE. "A multilevel logistic regression model for the analyses of concurrent Human papillomavirus (HPV) infections." Doctoral thesis, Università degli Studi di Milano, 2007. http://hdl.handle.net/2434/33629.
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Human Papillomavirus (HPV) is a sexually transmitted infection that causes cervical cancer. A nested three-level logistic regression model was introduced in order to investigate whether, in the IARC HPV prevalence surveys, co-infection with different HPV types occurs more or less frequently than expected if the infections are independent from one another. Two random effects, at individual and study-area level, were specified, while the fixed-effect covariates at individual level were age and lifetime number of sexual partners. The Best Linear Unbiased Predictors (BLUP) technique was used to estimate the random components. The predictions of the random effects at individual level are particularly important because they can be considered as a synthetic estimate of all those residual sources of individual variability, i.e., unmeasured risk factors due to sexual habits, that otherwise could not be accounted for. Individual probabilities of being positive for each HPV type are thus estimated, and the expected vs observed number of infections are compared, given the positivity for a different HPV type. Few positive associations (HPV58 with 33 being the strongest) were found in this analyses. However, the majority of HPV types, particularly the two most oncogenic types, HPV16 and 18, that are also included in the prophylactic vaccine, were not associated with one another.
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Erich, Roger Alan. "Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1342796812.
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Chang, Wei-Te. "The analysis of random effects regression model for predicting the shelf-life of gun propellant." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1995. http://handle.dtic.mil/100.2/ADA295246.
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