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1

Teng, Yunlong, and Yingrui Zhao. "Statistics in Ella Mathematics." Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-21475.

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"Ella Mathematics" is a web-based e-learning system which aims to improve elementary school students’ mathematics learning in Sweden. Such an e-learning tool has been partially completed in May 2012, except descriptive statistics module summarizing students’ performance in the learning process. This project report presents and describes the design and implementation of such descriptive statistics module, which intends to allow students to check their own grades and learning progress; teachers to check and compare students’ grades and progress, as well as parents to compare their children’s grades and learning progress with the average grade and progress of other students. To better understand and design such functionalities, different mathematical e-learning systems were investigated. Another contribution of this project relates to the evaluation and redesign of the existing database model of the “Ella Mathematics” system. The redesign improved performance and reduced data redundancy.
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2

Liu, Fangda, and 刘芳达. "Two results in financial mathematics and bio-statistics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46976437.

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3

Dumitriu, Ioana 1976. "Eigenvalue statistics for beta-ensembles." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29347.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 155-163) and index.
Random matrix theory is a maturing discipline with decades of research in multiple fields now beginning to converge. Experience has shown that many exact formulas are available for certain matrices with real, complex, or quaternion entries. In random matrix jargon, these are the cases β = 1, 2 and 4 respectively. This thesis explores the general P > 0 case mathematically and with symbolic software. We focus on generalizations of the Hermite distributions originating in physics (the "Gaussian" ensembles) and the Laguerre distributions of statistics (the "Wishart" matrices). One of our main contributions is the construction of tridiagonal matrix models for the general (β > 0) 0 β-Hermite and (β > 0, a > β(m - 1)/2) β-Laguerre ensembles of parameter a and size m, and investigate applications of these new ensembles, particularly in the areas of eigenvalue statistics. The new models are symmetric tridiagonal, and with entries from real distributions, regardless of the value of β. The entry distributions are either normal or X, so "classical", and the independence pattern is maximal, in the sense that the only constraints arise from the symmetric/semi-definite condition. The β-ensemble distributions have been studied for the particular 1, 2, 4 values of p as joint eigenvalue densities for full random matrix ensembles (Gaussian, or Hermite, and Wishart, or Laguerre) with real, complex, and quaternion entries (for references, see [66] and [70]). In addition, general -ensembles were considered and studied as theoretical distributions ([8, 51, 50, 55, 56]), with applications in lattice gas theory and statistical mechanics (the parameter being interpreted as an arbitrary inverse temperature of a Coulomb gas with logarithmic potential).
(cont.) Certain eigenvalue statistics over these general β-ensembles, namely those expressible in terms of integrals of symmetric polynomials with corresponding Hermite or Laguerre weights, can be computed in terms of multivariate orthogonal polynomials (Hermite or Laguerre). We have written a Maple Library (MOPs: Multivariate Orthogonal Polynomials symbolically) which implements some new and some known algorithms for computing the Jack, Hermite, Laguerre, and Jacobi multivariate polynomials for arbitrary. This library can be used as a tool for conjecture-formulation and testing, for statistical computations, or simply for getting acquainted with the mathematical concepts. Some of the figures in this thesis have been obtained using MOPs. Using the new β-ensemble models, we have been able to provide a unified perspective of the previously isolated 1, 2, and 4 cases, and prove generalizations for some of the known eigenvalue statistics to arbitrary β. We have rediscovered (in the Hermite case) a strong version of the Wigner Law (semi-circle), and proved (in the Laguerre case) a strong version of the similar law (generalized quarter-circle). We have obtained first-order perturbation theory for the P large case, and we have reason to believe that the tridiagonal models in the large n (ensemble size) limit will also provide a link between the largest eigenvalue distributions for both Hermite and Laguerre for arbitrary P (for β = 1, 2, this link was proved to exist by Johannson [52] and Johnstone [53]) ...
by Ioana Dumitriu.
Ph.D.
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4

Elizalde, Sergi 1979. "Statistics on pattern-avoiding permutations." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16629.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 111-116).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
This thesis concerns the enumeration of pattern-avoiding permutations with respect to certain statistics. Our first result is that the joint distribution of the pair of statistics 'number of fixed points' and 'number of excedances' is the same in 321-avoiding as in 132-avoiding permutations. This generalizes a recent result of Robertson, Saracino and Zeilberger, for which we also give another, more direct proof. The key ideas are to introduce a new class of statistics on Dyck paths, based on what we call a tunnel, and to use a new technique involving diagonals of non-rational generating functions. Next we present a new statistic-preserving family of bijections from the set of Dyck paths to itself. They map statistics that appear in the study of pattern-avoiding permutations into classical statistics on Dyck paths, whose distribution is easy to obtain. In particular, this gives a simple bijective proof of the equidistribution of fixed points in the above two sets of restricted permutations.
(cont.) Then we introduce a bijection between 321- and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. A part of our bijection is based on the Robinson-Schensted-Knuth correspondence. We also show that our bijection preserves additional parameters. Next, motivated by these results, we study the distribution of fixed points and excedances in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving generating functions which enumerate them. Some cases are generalized to patterns of arbitrary length. For avoidance of one single pattern we give partial results. We also describe the distribution of these statistics in involutions avoiding any subset of patterns of length 3. The main technique consists in using bijections between pattern-avoiding permutations and certain kinds of Dyck paths, in such a way that the statistics in permutations that we consider correspond to statistics on Dyck paths which are easier to enumerate. Finally, we study another kind of restricted permutations, counted by the Motzkin numbers. By constructing a bijection into Motzkin paths, we enumerate them with respect to some parameters, including the length of the longest increasing and decreasing subsequences and the number of ascents.
by Sergi Elizalde.
Ph.D.
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5

Hofbauer, Pamela S. Mooney Edward S. "Characterizing high school students' understanding of the purpose of graphical representations." Normal, Ill. : Illinois State University, 2007. http://proquest.umi.com/pqdweb?index=0&did=1414114601&SrchMode=1&sid=6&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1207664408&clientId=43838.

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Thesis (Ph. D.)--Illinois State University, 2007.
Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Edward S. Mooney (chair), Cynthia W. Langrall, Sherry L. Meier, Norma C. Presmeg. Includes bibliographical references (leaves 112-121) and abstract. Also available in print.
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6

Doyle, Philip Gerard. "Developing statistical literacy with students and teachers in the secondary mathematics classroom." The University of Waikato, 2008. http://hdl.handle.net/10289/2324.

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This thesis investigates the teaching of statistical literacy in the first two years of secondary school mathematics. The teachers involved in the research aim to make changes to classroom practice in the teaching and learning of statistics and statistical literacy in response to changes in the New Zealand curriculum. An action research methodology is adopted by the research. A group of three teachers and the author undertake an action research cycle of planning, observing, acting and reflecting in three different Year 9 and 10 mathematics classrooms. The research documents the designing and implementing of strategies by a group of teachers in a mathematics department for integrating statistical literacy into teaching programmes. The research adopts framework for improving practice that utilise models for statistical literacy and thinking and principles for teaching with a language learning or literacy focus. Data is collected through discussions with teachers, observations of lessons and interviews with teachers and students. Themes emerge from the data. They include the significance of teacher and student concepts of statistics and statistical literacy, the importance of language and literacy in the statistics classroom, the adoption of teaching principles to facilitate statistical literacy and the challenge of adopting a critical literacy stance in the statistics classroom. The study highlights the importance of literacy and language skills in statistical literacy. The research concludes that the important changes needed for developing statistical literacy are about classroom methodology rather than content knowledge and shows that adoption of language learning principles into the teaching programme may achieve this.
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7

Leong, Jennifer. "High School Students' Attitudes and Beliefs Regarding Statistics in a Service-Learning-Based Statistics Course." Digital Archive @ GSU, 2007. http://digitalarchive.gsu.edu/msit_diss/12.

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Despite agreement among researchers about the powerful influence of attitudes and beliefs on the development of students’ mathematical knowledge base (Leder, Pehkonen, & Törner, 2002), relatively little is known about these constructs in statistics education. This study investigated the relationship between mathematics-and statistics-related attitudes and beliefs of 11 high school students in an introductory statistics course designed around a 13-week long service-learning project. Service-learning is a pedagogical approach that situates academic learning in the context of community service. The study utilized qualitative, teacher-researcher (Cochran-Smith & Lytle, 1993) methodology from an interpretivist perspective. The three primary modes of data collection were journals, narratives, and an open-ended survey (Survey of Mathematical and Statistical Affect). Observations and reflections were also recorded regularly in a researcher journal. Inquiry adhered to guidelines for trustworthiness and rigor as outlined by Lincoln and Guba (1985). Item, pattern, and structural levels of analysis were employed (LeCompte and Schensul, 1999b). Investigation into attitudes and beliefs was framed in accordance with Op t’ Eynde, De Corte, and Verschaffel’s (2002) conceptualization of the mathematics-related belief system and McLeod’s (1992) framework of the affective domain in mathematics education. Results indicate that participants’ attitudes toward mathematics and statistics tended to converge while participants’ beliefs regarding mathematics and statistics tended to diverge. Participants like mathematics and statistics that involve real-life scenarios. Participants also like mathematics and statistics that do not require complex mathematical tasks. Participants’ beliefs regarding statistics were generally more positive than beliefs regarding mathematics. Participants reported greater confidence doing statistics than mathematics and contribute this confidence, in part, to service-learning. Participants also experienced a heightened sense of social awareness and social responsibility through the service-learning project. These results provide evidence that service-learning can be utilized to solidify positive attitudes and beliefs regarding statistics among high school students, in spite of potentially less positive ones toward mathematics.
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8

Bourget, Alain. "Nodal statistics for the Lame ensemble." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37872.

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The Lame polynomials naturally arise when separating variables in Laplace's equation in elliptic-spherical coordinates. The products of these polynomials form a class of spherical harmonics, which are the joint eigenfunctions of a quantum completely integrable system of commuting, second-order differential operators P0 = DSN , P2,..., PN -1 acting on Cinfinity( SN ). These operators depend on parameters and thus constitute an ensemble.
In the main result presented in this thesis, we compute the limiting mean level spacings distribution for the zeroes of Lame polynomials in various thermodynamic, asymptotic regimes. We give results both in the mean and pointwise, for an asymptotically full set of values of the parameters. As an application, we compute the limiting level spacings distribution of the zeroes of Van Vleck polynomials.
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9

He, Siqian. "Statistics and dynamics of stiff chains." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38400.

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10

Ko, Byeonggeon, and Yang Gao. "Monitoring Exchange Rates by Statistical Process Control." Thesis, Högskolan i Halmstad, Tillämpad matematik och fysik (MPE-lab), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-16533.

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The exchange rate market has traditionally played a key role in the financial market. The variation of the exchange rate which is called volatility is also an important feature for studying the exchange rate market because the increased volatility may have a negative effect on a nation's economy by increasing the uncertainty in the exchange market. In this paper the volatility of the exchange rate is considered by means of a Heterogeneous Autoregression Conditional Heteroskedastictity (HARCH) Model. It explains the volatility of the exchange rate market well. In addition, it is assumed that at a random time point a change of a parameter in the distribution of the random process underobservation may occur. Some methods such as the Shewhart method, the Culumative Sum Method (CUSUM) and the ExponentiallyWeighted Moving Average Method (EWMA) are investigated within the frames of this change-point problem. In order to evaluate them, Average Run Length (ARL) and Conditional Expected Delay (CED) will be used asperformance measures.
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11

Steingrímsson, Einar. "Permutations statistics of indexed and poset permutations." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/35952.

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12

Ma, Yanyuan 1970. "Studies in matrix perturbation and robust statistics." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85305.

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13

Degenhardt, Sheldon. "Weighted-inversion statistics and their symmetry groups /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487941504293867.

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14

Molin, Camilla. "A statistical analysis of the performance in mathematics of secondary students in Portugal." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-418811.

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15

Fok, Hou Kei. "Generalizations of some Hermite-Hadamard-type inequalities." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592934.

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16

Barrow, John H. "Revising the BGSU Mathematics Placement System." Bowling Green State University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1245699733.

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17

Thayne, Jeffrey L. "Making statistics matter| Self-data as a possible means to improve statistics learning." Thesis, Utah State University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10250713.

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Research has demonstrated that well into their undergraduate and even graduate education, learners often struggle to understand basic statistical concepts, fail to see their relevance in their personal and professional lives, and often treat them as little more than mere mathematics exercises. Undergraduate learners often see statistical concepts as means to passing exams, completing required courses, and moving on with their degree, and not as instruments of inquiry that can illuminate their world in new and useful ways.

This study explored ways help learners in an undergraduate learning context to treat statistical inquiry as mattering in a practical research context, by inviting them to ask questions about and analyze large, real, messy datasets that they have collected about their own personal lives (i.e., self -data). This study examined the conditions under which such an intervention might (and might not) successfully lead to a greater sense of the relevance of statistics to undergraduate learners. The goal is to place learners in a context where their relationship with data analysis can more closely mimic that of disciplinary professionals than that of students with homework; that is, where they are illuminating something about their world that concerns them for reasons beyond the limited concerns of the classroom.

The study revealed five themes in the experiences of learners working with self-data that highlight contexts in which data-analysis can be made to matter to learners (and how self-data can make that more likely): learners must be able to form expectations of the data, whether based on their own experiences or external benchmarks; the data should have variation to account for; the learners should treat the ups and downs of the data as more or less preferable in some way; the data should address or related to ongoing projects or concerns of the learner; and finally, learners should be able to investigate quantitative or qualitative covariates of their data. In addition, narrative analysis revealed that learners using self-data treated data analysis as more than a mere classroom exercise, but as exercises in inquiry and with an invested engagement that mimicked (in some ways) that of a disciplinary professional.

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18

Hua, Hairui. "Survival modelling in mathematical and medical statistics." Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5808/.

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An essential aspect of survival analysis is the estimation and prediction of survival probabilities for individuals. For this purpose, mathematical modelling of the hazard rate function is a fundamental issue. This thesis focuses on the novel estimation and application of hazard rate functions in mathematical and medical research. In mathematical research we focus on the development of a semiparametric kernel-based estimate of hazard rate function and a L\(_1\) error optimal kernel hazard rate estimate. In medical research we concentrate on the development and validation of survival models using individual participant data from multiple studies. We also consider how to fit survival models that predict individual response to treatment effectiveness, given IPD from multiple trials.
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Emmioglu, Esma. "A Structural Equation Model Examining The Relationships Among Mathematics Achievement, Attitudes Toward Statistics, And Statistics Outcomes." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613751/index.pdf.

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The purpose of the current study was to investigate the structural relationships among self-reported mathematics achievement, attitudes toward statistics, and statistics outcomes by testing a structural model. The current study utilized a survey design. The participants of study consisted of 247 undergraduate and graduate students enrolled in statistics courses in a university in Turkey. The participants were from different disciplines such as engineering, education, and economics. The Turkish version of the Survey of Attitudes toward Statistics-36©
(SATS-36©
) was used to collect data. The SATS-36©
assessed six components of statistics attitudes: cognitive competence, value, difficulty, effort, interest, and affect. Higher scores of the six components referred to the more positive attitudes. In addition, the SATS-36©
involved additional items to measure students&rsquo
self-reports of mathematics achievement and statistics outcomes. Results of the descriptive statistics analyses revealed that participants of the study had positive attitudes toward statistics except that they had neutral perceptions about the difficulty of statistics and neutral interest in statistics. Statistics outcomes variable was significantly correlated with mathematics achievement, affect, value, interest, and effort variables. Structural equation modeling was used to test the hypothesized structural regression model. Results indicated that affect, value, cognitive competence, and interest variables had large total standardized effects on statistics outcomes variable. Mathematics achievement and the effort variables had small total effects on explaining statistics outcomes. Difficulty had no statistically significant total effect on explaining statistics outcomes. Overall, the hypothesized structural regression model explained 66% of the total variance in statistics outcomes, which was statistically significant.
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20

Marriott, Paul. "Applications of differential geometry to statistics." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/55719/.

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Chapters 1 and 2 are both surveys of the current work in applying geometry to statistics. Chapter 1 is a broad outline of all the work done so far, while Chapter 2 studies, in particular, the work of Amari and that of Lauritzen. In Chapters 3 and 4 we study some open problems which have been raised by Lauritzen's work. In particular we look in detail at some of the differential geometric theory behind Lauritzen's defmition of a Statistical manifold. The following chapters follow a different line of research. We look at a new non symmetric differential geometric structure which we call a preferred point manifold. We show how this structure encompasses the work of Amari and Lauritzen, and how it points the way to many generalizations of their results. In Chapter 5 we define this new structure, and compare it to the Statistical manifold theory. Chapter 6 develops some examples of the new geometry in a statistical context. Chapter 7 starts the development of the pure theory of these preferred point manifolds. In Chapter 8 we outline possible paths of research in which the new geometry may be applied to statistical theory. We include, in an appendix, a copy of a joint paper which looks at some direct applications of differential geometry to a statistical problem, in this case it is the problem of the behaviour of the Wald test with nonlinear restriction functions.
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21

Audibert, Jean-Yves. "PAC-Bayesian aggregation and multi-armed bandits." Habilitation à diriger des recherches, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00843972.

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This habilitation thesis presents several contributions to (1) the PAC-Bayesian analysis of statistical learning, (2) the three aggregation problems: given d functions, how to predict as well as (i) the best of these d functions (model selection type aggregation), (ii) the best convex combination of these d functions, (iii) the best linear combination of these d functions, (3) the multi-armed bandit problems.
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22

Lodhia, Asad. "Topics in linear spectral statistics of random matrices." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112898.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 78-83).
The behavior of the spectrum of a large random matrix is a topic of great interest in probability theory and statistics. At a global level, the limiting spectra of certain random matrix models have been known for some time. For example, the limiting spectral measure of a Wigner matrix is a semicircle law and the limiting spectral measure of a sample covariance matrix under certain conditions is a Marc̆enko-Pastur law. The local behavior of eigenvalues for specific random matrix ensembles (GUE and GOE) have been known for some time as well and until recently, were conjectured to be universal. There have been many recents breakthroughs in the universality of this local behavior of eigenvalues for Wigner Matrices. Furthermore, these universality results laws have been proven for other probabilistic models of particle systems, such as Beta Ensembles. In this thesis we investigate the fluctuations of linear statistics of eigenvalues of Wigner Matrices and Beta Ensembles in regimes intermediate to the global regime and the microscopic regime (called the mesoscopic regime). We verify that these fluctuations are Gaussian and derive the covariance for a range of test functions and scales. On a separate line of investigation, we study the global spectral behavior of a random matrix arising in statistics, called Kendall's Tau and verify that it satisfies an analogue of the Marc̆enko-Pastur Law.
by Asad Lodhia.
Ph. D.
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23

Stadler, Jonathan. "Schur functions, juggling, and statistics on shuffled permutations /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487947501135397.

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Connell, Matthew Aaron. "Generalized Laguerre Series for Empirical Bayes Estimation: Calculations and Proofs." Ohio University Honors Tutorial College / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1619179966891297.

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Seier, Edith, and Karl H. Joplin. "Introduction to STATISTICS in a Biological Context." Digital Commons @ East Tennessee State University, 2011. http://amzn.com/1463613377.

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Kritchevski, Evgenij. "Nodal statistics of Heine-Stieltjes and Van Vleck polynomials." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81348.

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We study the polynomial solutions of the Lame differential equation Azy'' z+2Bz y'z+C zyz=0 where A(z), B( z), C(z) ∈ C [z] are polynomials of degree N + 1, N and N - 1 respectively. We review classical results concerning the location of the zeros of y(z) and C(z) and their electrostatic interpretation. Asymptotic distribution of the zeros as the degree K of y(z) approaches infinity is then discussed. We also derive numerical methods that allow us to compute solutions of high degree K and present a variety of new fine experimental results such as the asymptotic nearest neighbor spacing distribution and the description of complex configurations.
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Bunge, John Arnold. "Distribution theory for record statistics from random record models /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487671108306781.

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Murphy, Sean. "Some topics in spatial probability and statistics." Thesis, University of Bath, 1989. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280810.

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Pedrick, Micah G. "Complexity of Linear Summary Statistics." Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/99.

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Families of linear functionals on a vector space that are mapped to each other by a group of symmetries of the space have a significant amount of structure. This results in computational redundancies which can be used to make computing the entire family of functionals at once more efficient than applying each in turn. This thesis explores asymptotic complexity results for a few such families: contingency tables and unranked choice data. These are used to explore the framework of Radon transform diagrams, which promise to allow general theorems about linear summary statistics to be stated and proved.
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Lochner, Michelle Aileen Anne. "New applications of statistics in astronomy and cosmology." Doctoral thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/12864.

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Over the last few decades, astronomy and cosmology have become data-driven fields. The parallel increase in computational power has naturally lead to the adoption of more sophisticated statistical techniques for data analysis in these fields, and in particular, Bayesian methods. As the next generation of instruments comes online, this trend should be continued since previously ignored effects must be considered rigorously in order to avoid biases and incorrect scientific conclusions being drawn from the ever-improving data. In the context of supernova cosmology, an example of this is the challenge from contamination as supernova datasets will become too large to spectroscopically confirm the types of all objects. The technique known as BEAMS (Bayesian Estimation Applied to Multiple Species) handles this contamination with a fully Bayesian mixture model approach, which allows unbiased estimates of the cosmological parameters. Here, we extend the original BEAMS formalism to deal with correlated systematics in supernovae data, which we test extensively on thousands of simulated datasets using numerical marginalization and Markov Chain Monte Carlo (MCMC) sampling over the unknown type of the supernova, showing that it recovers unbiased cosmological parameters with good coverage. We then apply Bayesian statistics to the field of radio interferometry. This is particularly relevant in light of the SKA telescope, where the data will be of such high quantity and quality that current techniques will not be adequate to fully exploit it. We show that the current approach to deconvolution of radio interferometric data is susceptible to biases induced by ignored and unknown instrumental effects such as pointing errors, which in general are correlated with the science parameters. We develop an alternative approach - Bayesian Inference for Radio Observations (BIRO) - which is able to determine the joint posterior for all scientific and instrumental parameters. We test BIRO on several simulated datasets and show that it is superior to the standard CLEAN and source extraction algorithms. BIRO fits all parameters simultaneously while providing unbiased estimates - and errors - for the noise, beam width, pointing errors and the fluxes and shapes of the sources.
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Kueh, Audrey. "Spherical wavelet techniques in nonparametric statistics." Thesis, University of Cambridge, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648593.

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Staplin, Natalie. "Informative censoring in transplantation statistics." Thesis, University of Southampton, 2012. https://eprints.soton.ac.uk/341789/.

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Observations are informatively censored when there is dependence between the time to the event of interest and time to censoring. When considering the time to death of patients on the waiting list for a transplant, particularly a liver transplant, patients that are removed for transplantation are potentially informatively censored, as generally the most ill patients are transplanted. If this censoring is assumed to be non-informative then any inferences may be misleading. The existing methods in the literature that account for informative censoring are applied to data to assess their suitability for the liver transplantation setting. As the amount of dependence between the time to failure and time to censoring variables cannot be identied from the observed data, estimators that give bounds on the marginal survival function for a given range of dependence values are considered. However, the bounds are too wide to be of use in practice. Sensitivity analyses are also reviewed as these allow us to assess how inferences are affected by assuming differing amounts of dependence and whether methods that account for informative censoring are necessary. Of the other methods considered IPCW estimators were found to be the most useful in practice. Sensitivity analyses for parametric models are less computationally intensive than those for Cox models, although they are not suitable for all sets of data. Therefore, we develop a sensitivity analysis for piecewise exponential models that is still quick to apply. These models are exible enough to be suitable for a wide range of baseline hazards. The sensitivity analysis suggests that for the liver transplantation setting the inferences about time to failure are sensitive to informative censoring. A simulation study is carried out that shows that the sensitivity analysis is accurate in many situations, although not when there is a large proportion of censoring in the data set. Finally, a method to calculate the survival benefit of liver transplantation is adapted to make it more suitable for UK data. This method calculates the expected change in post-transplant mortality relative to waiting list mortality. It uses IPCW methods to account for the informative censoring encountered when estimating waiting list mortality to ensure the estimated survival benefit is as accurate as possible.
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Ijeh, Sunday Bomboi. "How competent mathematics teachers develop pedagogical content knowledge in statistics teaching." Thesis, University of Pretoria, 2012. http://hdl.handle.net/2263/24074.

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This study is concerned with how competent mathematics teachers develop pedagogical content knowledge (PCK) in statistics teaching. Pedagogical content knowledge was used as the theoretical framework that guided the research and data collection. The study’s methodology consisted of two phases. In the first phase, the six identified mathematics teachers undertook a conceptual knowledge written exercise. The result of this exercise was used to select the best four performing teachers for the second phase of the study. The second phase consisted mainly of lesson observations, interviews, written documents in the form of completed questionnaires, written diaries or reports, document analysis designed to produce rich detailed descriptions of participating teachers’ PCK in the context of teaching statistics concepts at school level. The concept mapping exercise was used to indirectly assess participating teachers’ content knowledge and their conceptions of the nature of school statistics and how it is to be taught. The qualitative data obtained were analysed to try to determine individual teachers’ content knowledge of school statistics, related pedagogical knowledge, knowledge of learners’ conceptions in statistics teaching, knowledge of learners’ learning difficulties as well as how they developed their PCK in statistics teaching. The analysis was done based on iterative coding and categorisation of responses and observations made to identify themes, patterns, and gaps, in school statistics teaching. Commonalities and differences if any, in the PCK profiles of the four participating teachers were also analysed and determined. The results of the study showed that overall, individual teachers develop their PCK in school statistics teaching by: (a) formally developing their knowledge of the subject matter in a formal undergraduate educational programme, as well as subject matter content knowledge during classroom practice; (b) using varied topic-specific instructional skills such as graphical construction skills in teaching statistical graphs; (c) using diagnostic techniques (oral questioning and pre-activity, class discussions and questioning) and a review of previous lessons to introduce lessons, and to determine learners’ preconceptions in statistics teaching ; (d) Using teaching strategies that can help to identify learners’ learning difficulties as well as intervention to address the difficulties; (e) continually updating their knowledge of school statistics by attending content knowledge workshops and other teacher development programmes designed to improve content knowledge and practice.
Thesis (PhD)--University of Pretoria, 2012.
Science, Mathematics and Technology Education
unrestricted
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34

Hendricks, Deborah J. "The use of propositional structures and subgoals in solving multi-step college statistical word and formula problems." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=531.

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Thesis (Ed. D.)--West Virginia University, 1999.
Title from document title page. Document formatted into pages; contains viii, 142 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 100-108).
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35

O'Keefe, Richard A. "Logic and lattices for a statistics advisor." Thesis, University of Edinburgh, 1987. http://hdl.handle.net/1842/26819.

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The work partially reported here concerned the development ot a prototype Expert System for giving advice about Statistics experiments, called ASA, and an inference engine to support ASA, called ABASE. This involved discovering what knowledge was necessary for performing the task at a satis? factory level of competence, working out how to represent this knowledge in a computer, and how to process the representations efficiently. Two areas of Statistical knowledge are described in detail: the classification of measure? ments and statistical variables, and the structure of elementary statistical experiments. A knowledge representation system based on lattices is proposed, and it is shown that such representations are learnable by computer programs, and lend themselves to particularly efficient implementation. ABASE was influenced by MBASE, the inference engine of MECHO [Bundy et al 79a]. Both are theorem provers working on typed function-free Horn clauses, with controlled creation of new entities. Their type systems and proof procedures are radically different, though, and ABASE is "conversational" while MBASE is not.
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Raqab, Mohammad Zayed. "Predictors of future order statistics from type II censored samples /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487776801323161.

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37

Fakhouri, Onsi Joe 1983. "Constraining the QSO luminosity function using gravitational lensing statistics." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/32733.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (leaves 85-87).
In this thesis we use gravitational lensing statistics to constrain the QSO luminosity function at a variety of redshifts. We present a theoretical discussion of gravitational lensing statistics and illustrate how high resolution QSO imagery can be used to constrain the QSO luminosity function. We then discuss the selection and observation of the 1073 QSO exposures in our sample. The sample covers a redshift range of 0.7by Onsi Joe Fakhouri.
S.B.
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38

Li, Linda S. "Investigating Students' Perceptions and Achievement in a Traditional Versus Online Statistics Course." Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1586540082366323.

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39

Zhou, Da Sheng. "Eigenvalues statistics for restricted trace ensembles." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2182958.

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40

Kudla, Jakub. "Monte Carlo SimulationsMethods in Pricing AmericanType Options." Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-13988.

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The aim of this paper is to present simulation methods for the pricing of American financial instruments. Three methods are presented. Each differs from the others in it's approach to the problem and the method of finding a solution. We illustrate the variety of possible approaches that can be adopted when dealing with this complicated problem. The results of using these algorithms are compared with examples found in literature on the subject. We try to identify the factors that influence price estimators and provide some new results about the properties and distributions of those estimators. We show that even a simple variance reduction technique has a positive effect for these algorithms. The purpose of this paper is to present the effectiveness of a simulation method in pricing American options. This is contrary to the opinion often stated in articles and monographs that the simulation approach is not adequate for the task. We provide an overview and comparison of earlier methods proposed and follow this with an extended discussion. This paper sets the foundations for further research into use of these algorithms for multidimensional problems, where they may offer a substantial advantage over deterministic methods.
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Howard, Marylesa Marie. "Computational methods for support vector machine classification and large-scale Kalman filtering." Thesis, University of Montana, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3568109.

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The first half of this dissertation focuses on computational methods for solving the constrained quadratic program (QP) within the support vector machine (SVM) classifier. One of the SVM formulations requires the solution of bound and equality constrained QPs. We begin by describing an augmented Lagrangian approach which incorporates the equality constraint into the objective function, resulting in a bound constrained QP. Furthermore, all constraints may be incorporated into the objective function to yield an unconstrained quadratic program, allowing us to apply the conjugate gradient (CG) method. Lastly, we adapt the scaled gradient projection method to the SVM QP and compare the performance of these methods with the state-of-the-art sequential minimal optimization algorithm and MATLAB's built in constrained QP solver, quadprog. The augmented Lagrangian method outperforms other state-of-the-art methods on three image test cases.

The second half of this dissertation focuses on computational methods for large-scale Kalman filtering applications. The Kalman filter (KF) is a method for solving a dynamic, coupled system of equations. While these methods require only linear algebra, standard KF is often infeasible in large-scale implementations due to the storage requirements and inverse calculations of large, dense covariance matrices. We introduce the use of the CG and Lanczos methods into various forms of the Kalman filter for low-rank approximations of the covariance matrices, with low-storage requirements. We also use CG for efficient Gaussian sampling within the ensemble Kalman filter method. The CG-based KF methods perform similarly in root-mean-square error when compared to the standard KF methods, when the standard implementations are feasible, and outperform the limited-memory Broyden-Fletcher-Goldfarb-Shanno approximation method.

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42

Raissi, Maziar. "Multi-fidelity Stochastic Collocation." Thesis, George Mason University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3591697.

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Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as well as the need to develop efficient, scalable, stable and convergent computational methods for solving differential equations with random inputs. Stochastic Galerkin methods based on polynomial chaos expansions have shown superiority to other non-sampling and many sampling techniques. However, for complicated governing equations numerical implementations of stochastic Galerkin methods can become non-trivial. On the other hand, Monte Carlo and other traditional sampling methods, are straightforward to implement. However, they do not offer as fast convergence rates as stochastic Galerkin. Other numerical approaches are the stochastic collocation (SC) methods, which inherit both, the ease of implementation of Monte Carlo and the robustness of stochastic Galerkin to a great deal. However, stochastic collocation and its powerful extensions, e.g. sparse grid stochastic collocation, can simply fail to handle more levels of complication. The seemingly innocent Burgers equation driven by Brownian motion is such an example. In this work we propose a novel enhancement to stochastic collocation methods using deterministic model reduction techniques that can handle this pathological example and hopefully other more complicated equations like Stochastic Navier Stokes. Our numerical results show the efficiency of the proposed technique. We also perform a mathematically rigorous study of linear parabolic partial differential equations with random forcing terms. Justified by the truncated Karhunen-Loève expansions, the input data are assumed to be represented by a finite number of random variables. A rigorous convergence analysis of our method applied to parabolic partial differential equations with random forcing terms, supported by numerical results, shows that the proposed technique is not only reliable and robust but also very efficient.

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43

Ruffin, Michael. "User retention and classification in a mobile gaming environment." Thesis, California State University, Long Beach, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1527021.

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Game analytics is a fast growing field where game studios are allocating valuable resources to develop sophisticated statistical models to understand user behavior and monetization habits to optimize game play and performance. Game developers' ability to understand user retention allows for game features that will generate high engagement leading to stronger overall monetization and increased lifetimes of players.

One important industry adopted metric is the percentage of users who log back into the game one day after installation, otherwise known as a one-day retention. Although this is an important metric, game studios typically allocate little resources to determining what user transactions are typically conducted on the day of installation that drive a one-day retention.

In this project, we first conduct a cluster analysis in an attempt to uncover meaningful subgroups based on players' transaction history on their first day of installation. Secondly, we use various classification methods including decision trees, logistic regression, and k-Nearest Neighbor algorithm to determine which behaviors are important in identifying whether a new user will return the following day.

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44

John, Thomas T. Chen Pinyuen. "Selection procedures for lognormal populations." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2004. http://wwwlib.umi.com/cr/syr/main.

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45

Xu, Ximing. "The statistical analysis of generalized adjacency and GA-clusters." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/27657.

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In this thesis I study a parametrized definition of gene clusters that permits control over the trade-off between increasing gene content versus conserving gene order within a cluster. This is based on the notion of generalized adjacency, which is the property shared by any two genes no farther apart, in the linear order of a chromosome, than a fixed threshold parameter theta. We discuss the the statistical properties of generalized adjacency ( GA) and derive the limiting probability distribution of the number of GA for random genomes. We also propose a test for gene clusters satisfying the generalized adjacency criterion under the null hypothesis that the genes are ordered randomly along the genomes.
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Leger, Danielle. "A study of classification techniques." Thesis, University of Ottawa (Canada), 2009. http://hdl.handle.net/10393/28219.

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The following thesis studies both parametric and non parametric approaches to classification. Among the various methods which exist, three are developed in detail. They are the Bayes rule, classification based on kernel density estimation and Fisher's discriminant function applied to the ranked data. Furthermore, we propose a new classification rule based on ranks. A Monte Carlo simulation study is then performed to test this new method and compare it with the other three classification techniques. The simulations indicate that the new classification rule performs well in many cases and that it is most effective when the number of dimensions are high and few observations are available. In this particular situation, the new classification rule proposed had the lowest probability of misclassification.
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47

Htet, Maung Soe. "Airline Error Correction Model and Its Application to Forecast the California Carbon Monoxide, Precipitation, and Air Temperature." Thesis, Southeast Missouri State University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10617045.

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Environmental data such as carbon monoxide (CO), precipitation, air temperature, and traffic have recently drawn the attention of researchers. Several time series models such as Seasonal Autoregressive Integrated Moving Average (SARIMA) and Vector Autoregressive (VAR) models have been applied to forecast CO. A VAR model can study extrinsic and intrinsic variables together but it does not incorporate seasonality. An Airline model is a special case of SARIMA which uses only an intrinsic variable and incorporates seasonality. The purpose of this thesis is to propose a time series model which incorporates seasonality and uses an extrinsic variable to forecast an intrinsic variable. The model is called Airline Error Correction Model (AECM). This thesis uses AECM to forecast CO using traffic, precipitation and air temperature as extrinsic variables. The forecasts using different models of AECM are compared to forecasts using VAR and Airline models. The results of the study show that AECM does a better job on forecasting than VAR and Airline models.

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48

Buzaianu, Elena Mihaela. "Selection procedures for binomial populations." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2006. http://proquest.umi.com/login?COPT=REJTPTU0NWQmSU5UPTAmVkVSPTI=&clientId=3739.

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49

Alpargu, Gülhan. "The Kantorovich inequality, with some extensions and with some statistical applications." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23985.

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In this thesis we focus on the "Kantorovich Inequality": {t prime At cdot t prime A sp{-1}t} over({t prime t) sp2}} le {{( lambda sb1+ lambda sb{n}) sp2} over {4 lambda sb1 lambda sb{n}}}, here t is a real $n times 1$ vector and A is a real $n times n$ symmetric positive definite matrix, with $ lambda sb1$ and $ lambda sb{n},$ respectively, its (fixed) largest and smallest, necessarily positive, eigenvalues. We begin the thesis with five different proofs of the Kantorovich Inequality and continue by showing that it is equivalent to five closely related inequalities due, respectively, to Schweitzer (1914), Polya-Szego (1925), Krasnosel'skii-Krei n (1952), Cassels (1955) and Greub-Rheinboldt (1959). We also examine several related inequalities which admit the Kantorovich Inequality as a special case, including the Bloomfield-Watson-Knott Inequality, for which we give a proof based on that presented by Bloomfield and Watson (1975). We also show that there appears to be a lacuna in the "brief proof" given by Yang (1990). Some statistical applications conclude the thesis with special emphasis on the efficiency of the Ordinary Least Squares Estimator in the Gauss-Markov linear statistical model.
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50

Colomay, Harold K. (Harold Kenney). "A survey of a class of nonparametric two-sample tests for right censored failure time data /." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56645.

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This thesis takes an in-depth focus at a specific class of nonparametric two-sample procedures for right censored failure time data-standardized weighted log-rank (SWL) statistics. This family of tests comprises the very famous Gehan, Efron, and log-rank procedures. The first two of these reduce to the Wilcoxon test with censoring absent, while the third one is a censored data generalization of the Savage test. Two particular topics of interest to us are (1) the generation of SWL statistics as score tests within the context of some popular regression models, and (2) asymptotic and small-sample behavior.
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