This diploma thesis entitled "Environmental policy of the European Union and its impact on the environmental policy of the Slovak Republic" targets the environmental policy of these two entities, focusing on a specific area, namely waste management. Despite the fact that environmental policy did not belong to the original agenda of the European Union during its creation, today, due to the gradual development characterized in the first part of the work, the EU is a prominent player in this field. In other parts of the work we describe how Slovakia has gradually undergone a progressive change, ie Europeanization, through its involvement in EU policies. Based on the membership of the Slovak Republic in the European Union since 2004, the Slovak Republic has obligations and commitments, which shows the significant influence of the European Union, and thus the existing environmental policies of the Member States are no longer politically or legally separated from EU environmental policy. In addition to the goal of providing a comprehensive overview of the development of environmental policy of the both European Union and the Slovak Republic since its formation, the main goal is to analyze the implementation of waste management in the form of Framework Directive 2008/98 / EC on waste. This goal is based...

This study aimed to observe measurement invariance between community college students and university students in response to the Community of Inquiry (CoI) Survey instrument. Most studies of the CoI survey instruments have recorded and validated the instruments considering undergraduate or graduate students. This study sought to validate and prove the survey tool as a reliable instrument for the community college population. The study employed SEM and meta-analytic procedures to observe measurement invariance between a Monte Carlo generated general university sample population and the community college survey population. The findings are discussed, as well as the implications for CoI studies in the community college.

Dans ce travail, nous nous intéressons à l'inférence statistique dans deux modèles semi-paramétrique et non-paramétrique stratifiés de durées de vie censurées. Nous proposons tout d'abord une statistique de test d'ajustement pour le modèle de régression stratifié à risques proportionnels. Nous établissons sa distribution asymptotique sous l'hypothèse nulle d'un ajustement correct du modèle aux données. Nous étudions les propriétés numériques de ce test (niveau, puissance sous différentes alternatives) au moyen de simulations. Nous proposons ensuite une procédure permettant de stratifier le modèle à 1isques proportionnels suivant un seuil inconnu d'une variable de stratification. Cette procédure repose sur l'utilisation du test d'ajustement proposé précédemment. Une étude de simulation exhaustive est conduite pour évaluer les pe1fonnances de cette procédure. Dans une seconde partie de notre travail, nous nous intéressons à l'application du test du logrank stratifié dans un contexte de données manquantes (nous considérons la situation où les strates ne peuvent être observées chez tous les individus de l'échantillon). Nous construisons une version pondérée du logrank stratifié adaptée à ce problème. Nous en établissons la loi limite sous l'hypothèse nulle d'égalité des fonctions de risque dans les différents groupes. Les propriétés de cette nouvelle statistique de test sont évaluée au moyen de simulations. Le test est ensuite appliqué à un jeu de données médicales. / In this work, we are interested in the statistical inference in two semi-parametric and non-parametric stratified models for censored data. We first propose a goodnessof- fit test statistic for the stratified proportional hazards regression model. We establish its asymptotic distribution under the null hypothesis of a correct fit of the model. We investigate the numerical properties of this test (level, power under different alternatives) by means of simulations. Then, we propose a procedure allowing to stratify the proportional hazards model according to an unknown threshold in a stratification variable. This procedure is based on the goodness-of-fit test proposed earlier. An exhaustive simulation study is conducted to evaluate the performance of this procedure. In a second part of our work, we consider the stratified logrank test in a context of missing data (we consider the situation where strata can not be observed on all sample individuals). We construct a weighted version of the stratified logrank, adapted to this problem. We establish its asymptotic distribution under the null hypothesis of equality of the hazards functions in the different groups. The prope1ties of this new test statistic are assessed using simulatious. Finally, the test is applied to a medical dataset.

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This thesis investigates some problems related to the form and shape of statistical distributions with the main focus on goodness of fit and bump hunting. A bump is a distinctive characteristic of distributional shape. A search for bumps, or bump hunting, in a probability density function (PDF) has long been an important topic in statistical research. We introduce a new definition of a bump which relies on the notion of the curvature of a planar curve. We then propose a new method for bump hunting which is based on a kernel density estimator of the unknown PDF. The method gives not only the number of bumps but also the location of their centers and base points. In quantitative risk applications, the selection of distributions that properly capture upper tail behavior is essential for accurate modeling. We study tests of distributional form, or goodness-of-fit (GoF) tests, that assess simple hypotheses, i.e., when the parameters of the hypothesized distribution are completely specified. From theoretical and practical perspectives, we analyze the limiting properties of a family of weighted Cramér-von Mises GoF statistics W2 with weight function psi(t)=1/(1-t)^beta (for beta<=2) which focus on the upper tail. We demonstrate that W2 has no limiting distribution. For this reason, we provide a normalization of W2 that leads to a non-degenerate limiting distribution. Further, we study W2 for composite hypotheses, i.e., when distributional parameters must be estimated from a sample at hand. When the hypothesized distribution is heavy-tailed, we examine the finite sample properties of W2 under the Chen-Balakrishnan transformation that reduces the original GoF test (the direct test) to a test for normality (the indirect test). In particular, we compare the statistical level and power of the pairs of direct and indirect tests. We observe that decisions made by the direct and indirect tests agree well, and in many cases they become independent as sample size grows. / Thesis / Doctor of Philosophy (PhD)

The overarching goal of this thesis is to use distance covariance based methods to extend asymptotic results from the i.i.d. case to general time series settings. Accounting for dependence may make already difficult statistical inference all the more challenging. The distance covariance is an increasingly popular measure of dependence between random vectors that goes beyond linear dependence as described by correlation. It is defined by a squared integral norm of the difference between the joint and marginal characteristic functions with respect to a specific weight function. Distance covariance has the advantage of being able to detect dependence even for uncorrelated data. The energy distance is a closely related quantity that measures distance between distributions of random vectors. These statistics can be used to establish asymptotic limit theory for stationary ergodic time series. The asymptotic results are driven by the limit theory for the empirical characteristic functions. In this thesis we apply the distance covariance to three problems in time series modeling: (i) Independent Component Analysis (ICA), (ii) multivariate time series clustering, and (iii) goodness-of-fit using residuals from a fitted model. The underlying statistical procedures for each topic uses the distance covariance function as a measure of dependence. The distance covariance arises in various ways in each of these topics; one as a measure of independence among the components of a vector, second as a measure of similarity of joint distributions and, third for assessing serial dependence among the fitted residuals. In each of these cases, limit theory is established for the corresponding empirical distance covariance statistics when the data comes from a stationary ergodic time series. For Topic (i) we consider an ICA framework, which is a popular tool used for blind source separation and has found application in fields such as financial time series, signal processing, feature extraction, and brain imaging. The Structural Vector Autogregression (SVAR) model is often the basic model used for modeling macro time series. The residuals in such a model are given by e_t = A S_t, the classical ICA model. In certain applications, one of the components of S_t has infinite variance. This differs from the standard ICA model. Furthermore the e_t's are not observed directly but are only estimated from the SVAR modeling. Many of the ICA procedures require the existence of a finite second or even fourth moment. We derive consistency when using the distance covariance for measuring independence of residuals under the infinite variance case.Extensions to the ICA model with noise, which has a direct application to SVAR models when testing independence of residuals based on their estimated counterparts is also considered. In Topic (ii) we propose a novel methodology for clustering multivariate time series data using energy distance. Specifically, a dissimilarity matrix is formed using the energy distance statistic to measure separation between the finite dimensional distributions for the component time series. Once the pairwise dissimilarity matrix is calculated, a hierarchical clustering method is then applied to obtain the dendrogram. This procedure is completely nonparametric as the dissimilarities between stationary distributions are directly calculated without making any model assumptions. In order to justify this procedure, asymptotic properties of the energy distance estimates are derived for general stationary and ergodic time series. Topic (iii) considers the fundamental and often final step in time series modeling, assessing the quality of fit of a proposed model to the data. Since the underlying distribution of the innovations that generate a model is often not prescribed, goodness-of-fit tests typically take the form of testing the fitted residuals for serial independence. However, these fitted residuals are inherently dependent since they are based on the same parameter estimates and thus standard tests of serial independence, such as those based on the autocorrelation function (ACF) or distance correlation function (ADCF) of the fitted residuals need to be adjusted. We apply sample splitting in the time series setting to perform tests of serial dependence of fitted residuals using the sample ACF and ADCF. Here the first f_n of the n data points in the time series are used to estimate the parameters of the model. Tests for serial independence are then based on all the n residuals. With f_n = n/2 the ACF and ADCF tests of serial independence tests often have the same limit distributions as though the underlying residuals are indeed i.i.d. That is, if the first half of the data is used to estimate the parameters and the estimated residuals are computed for the entire data set based on these parameter estimates, then the ACF and ADCF can have the same limit distributions as though the residuals were i.i.d. This procedure ameliorates the need for adjustment in the construction of confidence bounds for both the ACF and ADCF, based on the fitted residuals, in goodness-of-fit testing. We also show that if f_n < n/2 then the asymptotic distribution of the tests stochastically dominate the corresponding asymptotic distributions for the true i.i.d. noise; the stochastic order gets reversed under f_n > n/2.

The aim of this thesis was to investigate the use of effect sizes to report the results of statistical credit rating models in a more practical way. Rating systems in the form of statistical probability models like logistic regression models are used to forecast the behaviour of clients and guide business in rating clients as “high” or “low” risk borrowers. Therefore, model results were reported in terms of statistical significance as well as business language (practical significance), which business experts can understand and interpret. In this thesis, statistical results were expressed as effect sizes like Cohen‟s d that puts the results into standardised and measurable units, which can be reported practically. These effect sizes indicated strength of correlations between variables, contribution of variables to the odds of defaulting, the overall goodness-of-fit of the models and the models‟ discriminating ability between high and low risk customers. / Statistics / M. Sc. (Statistics)

Les tests d’adéquation font partie des pratiques qu’ont les statisticiens pour prendre une décision concernant l’hypothèse de l’utilisation d’une distribution paramétrique pour un échantillon. Dans ce mémoire, une application du test d’adéquation basé sur la fonction caractéristique proposé par Jiménez-Gamero et al. (2009) est faite dans le cas de la loi de Poisson bivariée. Dans un premier temps, le test est élaboré dans le cas de l’adéquation à une loi de Poisson univariée et nous avons trouvé son niveau bon. Ensuite cette élaboration est étendue au cas de la loi de Poisson bivariée et la puissance du test est calculée et comparée à celle des tests de l’indice de dispersion, du Quick test de Crockett et des deux familles de tests proposés par Novoa-Muñoz et Jiménez-Gamero (2014). Les résultats de la simulation ont permis de constater que le test avait un bon niveau comparativement aux tests de l’indice de dispersion et au Quick test de Crockett et qu’il était généralement moins puissant que les autres tests. Nous avons également découvert que le test de l’indice de dispersion devrait être bilatéral alors qu’il ne rejette que pour de grandes valeurs de la statistique de test. Finalement, la valeur-p de tous ces tests a été calculée sur un jeu de données de soccer et les conclusions comparées. Avec une valeur-p de 0,009, le test a rejeté l’hypothèse que les données provenaient d’une loi de Poisson bivariée alors que les tests proposés par Novoa-Muñoz et Jiménez-Gamero (2014) donnaient une conclusion différente. / Our aim in this thesis is to conduct the goodness-of-fit test based on empirical characteristic functions proposed by Jiménez-Gamero et al. (2009) in the case of the bivariate Poisson distribution. We first evaluate the test’s behaviour in the case of the univariate Poisson distribution and find that the estimated type I error probabilities are close to the nominal values. Next, we extend it to the bivariate case and calculate and compare its power with the dispersion index test for the bivariate Poisson, Crockett’s Quick test for the bivariate Poisson and the two test families proposed by Novoa-Muñoz et Jiménez-Gamero (2014). Simulation results show that the probability of type I error is close to the claimed level and that it is generally less powerful than other tests. We also discovered that the dispersion index test should be bilateral whereas it rejects for large values only. Finally, the p-value of all these tests is calculated on a real dataset from soccer. The p-value of the test is 0,009 and we reject the hypothesis that the data come from a Poisson bivariate while the tests proposed by Novoa-Muñoz et Jiménez-Gamero (2014) leads to a different conclusion.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.