Les travaux effectués durant cette thèse ont pour but de pallier le problème des corrélations au sein des bases de données, particulièrement fréquentes dans le cadre industriel. Une modélisation explicite des corrélations par un système de sous-régressions entre covariables permet de pointer les sources des corrélations et d'isoler certaines variables redondantes. Il en découle une pré-sélection de variables sans perte significative d'information et avec un fort potentiel explicatif (la structure de sous-régression est explicite et simple). Un algorithme MCMC (Monte-Carlo Markov Chain) de recherche de structure de sous-régressions est proposé, basé sur un modèle génératif complet sur les données. Ce prétraitement ne dépend pas de la variable réponse et peut donc être utilisé de manière générale pour toute problématique de corrélations. Par la suite, un estimateur plug-in pour la régression linéaire est proposé pour ré-injecter l'information résiduelle de manière séquentielle sans souffrir des corrélations entre covariables. Enfin, le modèle génératif complet peut être utilisé pour gérer des valeurs manquantes dans les données. Cela permet l'imputation multiple des données manquantes, préalable à l'utilisation de méthodes classiques incompatibles avec la présence de valeurs manquantes. Le package R intitulé CorReg implémente les méthodes développées durant cette thèse. / This thesis was motivated by correlation issues in real datasets, in particular industrial datasets. The main idea stands in explicit modeling of the correlations between covariates by a structure of sub-regressions, that simply is a system of linear regressions between the covariates. It points out redundant covariates that can be deleted in a pre-selection step to improve matrix conditioning without significant loss of information and with strong explicative potential because this pre-selection is explained by the structure of sub-regressions, itself easy to interpret. An algorithm to find the sub-regressions structure inherent to the dataset is provided, based on a full generative model and using Monte-Carlo Markov Chain (MCMC) method. This pre-treatment does not depend on a response variable and thus can be used in a more general way with any correlated datasets. In a second part, a plug-in estimator is defined to get back the redundant covariates sequentially. Then all the covariates are used but the sequential approach acts as a protection against correlations. Finally, the generative model defined here allows, as a perspective, to manage missing values both during the MCMC and then for imputation. Then we are able to use classical methods that are not compatible with missing datasets. Once again, linear regression is used to illustrate the benefits of this method but it remains a pre-treatment that can be used in other contexts, like clustering and so on. The R package CorReg implements the methods created during this thesis.

This thesis considers the problem of estimating limited dependent variable models when the latent residuals are heteroskedastic normally distributed random variables. Commonly used estimators are generally inconsistent in such situations. Two estimation methods that allow consistent estimation of the parameters of interest are presented and shown to be consistent when the latent residuals are heteroskedastic of unknown form. Both estimators use recent advances in the econometric literature on nonparametric estimation and deal with the unknown form of heteroskedasticity by approximating the variance using a Fourier series type approximation. The first estimator is based on the method of maximum likelihood and involves maximising the likelihood function by choice of the parameters of the variance function approximation and the other parameters of interest. Consistency is shown to hold in the three most popular limited dependent variable models — the Probit, Tobit, and sample selection models — provided that the number of terms in the approximation increases with the sample size. The second estimator, which can be used to estimate the Tobit and sample selection models, is based on a two-step procedure, using Fourier series approximations in both steps. Consistency and asymptotic normality are proven under restrictions on the rate of increase of the number of parameters in the approximating functions. Finally, a small Monte Carlo experiment is conducted to examine the small sample properties of the estimators. The results show that the estimators perform quite well and in many cases reduce the bias, relative to the commonly used estimators, with little or no efficiency loss. / Arts, Faculty of / Vancouver School of Economics / Graduate

Not only basic research in sciences, but also medicine, law, and manufacturing need statistical techniques, including graphics, to assess disagreement. For some items or individuals ⍳ = 1,2,---,ո suppose that pairs (X⍳,Y⍳) denote each item's measurements by two distinct methods or by two observers, or X⍳ and Y⍳ may be initial and repeat measurement scores, with discrepancy D⍳ = X⍳ - Y⍳. Disagreement may be characterized by location and scale parameters of discrepancy distributions. The present work primarily addresses estimation of central tendency - relative bias or median discrepancy (or discrepancy rate in some instances). Most previous literature on "agreement" or "reliability" instead concerns X, Y correlation, which can be regarded as the complement of discrepancy variance. (There is ambiguity or confusion about concepts of "reliability" in the literature of various applications.) Discrepancies D₁, D₂, • • •, Dո in practice often violate assumptions of standard statistical models and methods that have been commonly applied in studies of agreement. In particular, both X⍳ and Y⍳ generally incorporate measurement errors. Further, these two measurement error distributions for the ⍳th item need not be the same; and both distributions could depend on the magnitude µ⍳, of the item being measured. Hence, for example, discrepancy D⍳ could have variance proportional to the size of the item; and in general D₁, D₂, • • •, Dո are not identically distributed. Finally, the selection of items ⍳ = 1,2, • • •, ո often is not random. To estimate median discrepancy, we consider nonparametric confidence intervals corresponding to Student t test, sign test, Wilcoxon signed rank test, or other permutation tests. Several criteria are developed to compare the performance of one procedure relative to another, including expected ratio of confidence interval lengths (related to Pitman asymptotic relative efficiency of tests) and relative variability of interval lengths. Theoretical calculations and Monte Carlo simulation results suggest different procedural preferences for random sampling from different distributions. For discrepancies distributed non-identically, but symmetrically about a common median value, mixture sampling is used as an approximate model. This approach is related to a "random walk" (rather than random sample) model of D₁, D₂, • • •, Dո proposed particularly for discrepancies between counting processes. We also emphasize graphic methods, especially plots of difference of Y - X versus average (X + Y)/2, for exploratory analysis of discrepancy data and to choose appropriate statistical models and numerical methods. Various data sets are analyzed as examples of the methodology. / Science, Faculty of / Statistics, Department of / Graduate

The purpose of this study was to investigate the theoretical concepts involving the relation of self-variables to anxiety.

This thesis is the synthesis of theoretical and experimental works performed in the area of quantum foundations, particularly on quantum correlations and experimental tests of multiplicative Bell inequalities. First we begin with a comprehensive theoretical work performed on the foundations of quantum mechanics, focusing on the puzzling concepts of quantum entanglement, and hidden variable theories. Specifically, we present a broad overview of different classes of hidden variable theories such as local, crypto-nonlocal, contextual and non-local theories, along with several Bell like inequalities for these theories, providing theoretical proofs based on quantum mechanics for the falsification of some of these theories. Second we present a body of experimental, and theoretical works performed on a new class of Bell inequalities, i.e., the multiplicative Bell inequalities. We experimentally report the observation of the Bell parameters close to the Tsirelson (quantum) limit, upto a large number of measurement devices $(n)$, and compare the results with a particular deterministic strategy. We also obtain classical bounds for some $n$, and report the experimental violation of these classical limits. We theoretically derive new richer bounds on the CHSH inequality (named after John Clauser, Michael Horne, Abnor Shimony and Richard Holt) and the multiplicative Bell parameter for $n=2$, based on the principle of ``relativistic independence'', and experimentally observe the distribution of Bell parameters as predicted by these bounds.

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