Abstract In a two-level hierarchical linear model(HLM2), the outcome as well as covariates may have missing values at any of the levels. One way to analyze all available data in the model is to estimate a multivariate normal joint distribution of variables, including the outcome, subject to missingness conditional on covariates completely observed by maximum likelihood(ML); draw multiple imputation (MI) of missing values given the estimated joint model; and analyze the hierarchical model given the MI [1,2]. The assumption is data missing at random (MAR). While this method yields efficient estimation of the hierarchical model, it often estimates the model given discrete missing data that is handled under multivariate normality. In this thesis, we evaluate how robust it is to estimate a hierarchical linear model given discrete missing data by the method. We simulate incompletely observed data from a series of hierarchical linear models given discrete covariates MAR, estimate the models by the method, and assess the sensitivity of handling discrete missing data under the multivariate normal joint distribution by computing bias, root mean squared error, standard error, and coverage probability in the estimated hierarchical linear models via a series of simulation studies. We want to achieve the following aim: Evaluate the performance of the method handling binary covariates MAR. We let the missing patterns of level-1 and -2 binary covariates depend on completely observed variables and assess how the method handles binary missing data given different values of success probabilities and missing rates. Based on the simulation results, the missing data analysis is robust under certain parameter settings. Efficient analysis performs very well for estimation of level-1 fixed and random effects across varying success probabilities and missing rates. MAR estimation of level-2 binary covariate is not well estimated when the missing rate in level-2 binary covariate is greater than 10%. The rest of the thesis is organized as follows: Section 1 introduces the background information including conventional methods for hierarchical missing data analysis, different missing data mechanisms, and the innovation and significance of this study. Section 2 explains the efficient missing data method. Section 3 represents the sensitivity analysis of the missing data method and explain how we carry out the simulation study using SAS, software package HLM7, and R. Section 4 illustrates the results and useful recommendations for researchers who want to use the missing data method for binary covariates MAR in HLM2. Section 5 presents an illustrative analysis National Growth of Health Study (NGHS) by the missing data method. The thesis ends with a list of useful references that will guide the future study and simulation codes we used.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Titel: The evaluation of different test protocol of pull up exercise as a maximum strenth test in Czech Republic soldiers Goals: The aim of this study is to compare different methodological ways during pull up exercise as a test of uper externities and back maximum strenght. And to assesed which load to use in case of test reason. Ant find out, what influence has the soldiers equipment on strenght test. Method: The study is based on an experiment consisting in the performance of different testing protocols, the same group of probands and subsequent comparison probands ordinal position in selected test methodologies. Selected tests, the maximum number of pull-ups with their own weight, the maximum number of pull-ups with essential military equipment (15 kg), the maximum number of pull-ups with 40% of your own body weight, the maximum load lifted in pull up excercise and the absolute pull up, which was calculated on the maximum load lifted . Use was basic statistics and serial correlation by Kendall correlation coefficient. Results: Test with military equipment (load weighing 15 kg) correlated with the test pull up with its own body weight value τr = 0.83 for statistical significance level α = 0.05. Test the pull up with 40% correlated with test pull up with their own body weight value τr = 0.72, for...

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles. Then, usually, a constant in every partition is fitted. While this is a simple and intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and independent variables may look. Or it may be that a certain model is assumed or of interest and there is a number of candidate variables that may non-linearily give rise to different model parameter values. We present an approach that combines generalized linear models with recursive partitioning that offers enhanced interpretability of classical trees as well as providing an explorative way to assess a candidate variable's influence on a parametric model. This method conducts recursive partitioning of a the generalized linear model by (1) fitting the model to the data set, (2) testing for parameter instability over a set of partitioning variables, (3) splitting the data set with respect to the variable associated with the highest instability. The outcome is a tree where each terminal node is associated with a generalized linear model. We will show the methods versatility and suitability to gain additional insight into the relationship of dependent and independent variables by two examples, modelling voting behaviour and a failure model for debt amortization. / Series: Research Report Series / Department of Statistics and Mathematics

La dernière période glaciaire est marquée par la présence de deux grandes calottes boréales recouvrant l’actuel Canada et le nord de l’Eurasie. Ces calottes constituent un élément actif du système climatique en interagissant avec les différentes composantes du système Terre. L’objectif de cette thèse est de déterminer par quels mécanismes les changements de circulation atmosphérique lors du dernier cycle glaciaire induisent potentiellement une téléconnexion entre les paléo-calottes de l’hémisphère nord. L’utilisation d’un modèle couplé climat-calotte simplifié m’a permis de tester séparément l’influence de la topographie et de l’albédo des calottes sur les champs de température et de précipitation lors du dernier cycle glaciaire, et de mettre en évidence le rôle de la circulation atmosphérique dans la synergie entre les paléo-calottes de l’hémisphère nord. Pour étudier plus en détail les mécanismes de cette interaction, l’utilisation d’un modèle de circulation générale s’est avérée nécessaire. J’ai tout d’abord effectué une inter-comparaison des modèles ayant participé à l’exercice PMIP3 pour le dernier maximum glaciaire (DMG). Cette inter-comparaison a permis d’illustrer l’impact des conditions glaciaires sur le décalage du courant-jet en Atlantique Nord et d’établir un lien entre ce décalage et les précipitations au sud de l’Europe. Enfin, à l’aide d’expériences idéalisées menées avec le modèle atmosphérique LMDZ, j’ai pu étudier le rôle de chacune des calottes dans les changements de circulation atmosphérique observés auDMG. Cette étude montre en particulier l’influence notable de la calotte nord-américaine sur le bilan de masse de surface de la calotte eurasienne. / The last glacial period is characterized by the presence of two large ice sheets covering Canada and North Eurasia. These ice sheets are a key element of the climatic system by interacting with all the components of the Earth system. The aim of this thesis is to determine by which mechanisms changes in atmospheric circulation may have induced a teleconnexionbetween the Northern hemisphere paleo-ice sheets. The use of a simplified coupled climate-ice sheet model allowed to test separately the influence of the ice-sheet topography and albedo on temperature and precipitation fields throughout the last glacial cycle and to highlight the role of atmospheric circulation within the synergy of past boreal ice sheets.To investigate in more details the underlying mechanisms, the use of a general circulation model was necessary.I therefore carried out an inter-comparisonof the PMIP3 models to examine the GCM responsesto glacial conditions. This work allowed to determinethe role of glacial conditions on the shift of the NorthAtlantic jet stream position and to establish a relationshipbetween this shift and the amount of precipitationover southern Europe. The last part of this thesisis devoted to the respective role of each ice sheeton atmospheric circulation changes observed underglacial conditions. To achieve this, I performed idealizedexperiments with the atmospheric circulationmodel LMDZ. The results highlight the key influenceof the North American ice sheet on the Eurasian icesheet surface mass balance.

Dans le contexte de l'estimation paramétrique, les performances d'un estimateur peuvent être caractérisées, entre autre, par son erreur quadratique moyenne (EQM) et sa résolution limite. La première quantifie la précision des valeurs estimées et la seconde définit la capacité de l'estimateur à séparer plusieurs paramètres. Cette thèse s'intéresse d'abord à la prédiction de l'EQM "optimale" à l'aide des bornes inférieures pour des problèmes d'estimation simultanée de paramètres aléatoires et non-aléatoires (estimation hybride), puis à l'extension des bornes de Cramér-Rao pour des modèles d'observation moins standards. Enfin, la caractérisation des estimateurs en termes de résolution limite est également étudiée. Ce manuscrit est donc divisé en trois parties :Premièrement, nous complétons les résultats de littérature sur les bornes hybrides en utilisant deux bornes bayésiennes : la borne de Weiss-Weinstein et une forme particulière de la famille de bornes de Ziv-Zakaï. Nous montrons que ces bornes "étendues" sont plus précises pour la prédiction de l'EQM optimale par rapport à celles existantes dans la littérature.Deuxièmement, nous proposons des bornes de type Cramér-Rao pour des contextes d'estimation moins usuels, c'est-à-dire : (i) Lorsque les paramètres non-aléatoires sont soumis à des contraintes d'égalité linéaires ou non-linéaires (estimation sous contraintes). (ii) Pour des problèmes de filtrage à temps discret où l'évolution des états (paramètres) est régit par une chaîne de Markov. (iii) Lorsque la loi des observations est différente de la distribution réelle des données.Enfin, nous étudions la résolution et la précision des estimateurs en proposant un critère basé directement sur la distribution des estimées. Cette approche est une extension des travaux de Oh et Kashyap et de Clark pour des problèmes d'estimation de paramètres multidimensionnels. / In the parametric estimation context, estimators performances can be characterized, inter alia, by the mean square error and the resolution limit. The first quantities the accuracy of estimated values and the second defines the ability of the estimator to allow a correct resolvability. This thesis deals first with the prediction the "optimal" MSE by using lower bounds in the hybrid estimation context (i.e. when the parameter vector contains both random and non-random parameters), second with the extension of Cramér-Rao bounds for non-standard estimation problems and finally to the characterization of estimators resolution. This manuscript is then divided into three parts :First, we fill some lacks of hybrid lower bound on the MSE by using two existing Bayesian lower bounds: the Weiss-Weinstein bound and a particular form of Ziv-Zakai family lower bounds. We show that these extended lower bounds are tighter than the existing hybrid lower bounds in order to predict the optimal MSE.Second, we extend Cramer-Rao lower bounds for uncommon estimation contexts. Precisely: (i) Where the non-random parameters are subject to equality constraints (linear or nonlinear). (ii) For discrete-time filtering problems when the evolution of states are defined by a Markov chain. (iii) When the observation model differs to the real data distribution.Finally, we study the resolution of the estimators when their probability distributions are known. This approach is an extension of the work of Oh and Kashyap and the work of Clark to multi-dimensional parameters estimation problems.

O objetivo deste estudo foi definir e comparar os números e tipos de contatos oclusais em máxima intercuspidação. A pesquisa consistiu na análise clínica e fotográfica dos contatos oclusais em máxima intercuspidação, de 26 pacientes brasileiros, 20 do gênero masculino e 6 do gênero feminino, leucodermas, com idade média entre 12 e 18 anos, ao início do tratamento ortodôntico. Os pacientes foram diagnosticados e agrupados em 13 com maloclusão Classe I e 13 com maloclusão Classe II divisão 1ª, obedecendo aos seguintes critérios: Dentadura permanente de segundo molar esquerdo a segundo molar direito, tanto na maxila quanto na mandíbula, sem extrações dentárias, sem perda de material dentário por restaurações extensas, lesão cariosa, fraturas ou desgaste interproximal, sem tratamento ortodôntico prévio e desordem têmporo-mandibular. Após análise, os contatos oclusais foram classificados segundo os critérios estabelecidos como: tripodismo, bipodismo, monopodismo, cúspide a uma crista marginal, cúspide a duas cristas marginais, ponta de cúspide a plano inclinado oposto, superfície a superfície e topo a topo. O teste de Kolmogorov-Smirnov Z foi utilizado pra determinar normalidade e homogeneidade das variáveis e o teste t pareado para comparar as diferenças estatísticas das médias aritméticas dos contatos oclusais entre as maloclusões estudadas (p<.05). Os resultados obtidos permitiram concluir que o número médio de contatos oclusais por paciente na maloclusão Classe I foi de 43,38 e na maloclusão Classe II-1 de 44,38, sendo esta diferença estatisticamente não significativa. Os tipos e freqüências de contatos oclusais em MIC, na maloclusão Classe I, caracterizam-se em relação cúspide-fossa (32%) (3% de tripodismo, 14% bipodismo, 15% monopodismo), cúspide a uma crista marginal (21%), cúspide a duas cristas (14%), cúspide a um plano inclinado (11%), superficie a superficie (22%) e topo a topo (1%). Na maloclusão Classe II-1, caracterizam-se em relação cúspide-fossa (34%) (4% de tripodismo, 11% bipodismo, 19% monopodismo), cúspide a uma crista marginal (14%), cúspide a duas cristas (13%), cúspide a um plano inclinado (10%), superficie a superficie (30%) e topo a topo (0,4%). Após este estudo podemos afirmar que, entre uma maloclusão Classe I e Classe II-1 de Angle, existe uma diversidade de fatores que influenciam no número de contatos oclusais. Concluindo a não existência de uma padronização dos tipos de contatos oclusais de acordo com as maloclusões estudadas. Uma adequada seleção de um padrão cúspide-fossa ou cúspide-crista marginal e a sua localização nos dentes, pode ser modificada de acordo com as exigências de cada caso individualmente. A existência de contatos oclusais adequados permite uma correta distribuição de forças mastigatórias, promovendo saúde periodontal. / The aim of this study was to define and compare numbers and types of occlusal contacts in maximum intercuspidation. The study consisted of clinical and photographic analysis of occlusal contacts in maximum intercuspidation. Twenty-six Brazilian subjects were selected before orthodontic treatment, 20 males and 6 females, leucodermas with ages ranging between 12 and 18 years. The subjects were diagnosed and grouped into 13 with Angle Class I malocclusion and 13 with Angle Class II division 1 malocclusion, according to the following criteria: complete permanent dentition erupted from second molar to second molar, without cavities, interproximal wear, extractions or previous orthodontic treatment, healthy periodontal status and absence of temporo-mandibular joint dysfunction. After analysis, the occlusal contacts were classified according to the established criteria as: tripodism, bipodism, monopodism, cuspid to a marginal ridge, cuspid to two marginal ridges, cuspid tip to inclined plane, surface to surface and top to top. The Kolmogorov- Smirnov Z test was used to determine variables normality and paired t test to compare occlusal contacts statistical differences between the studied malocclusions (p<.05). The results showed that the mean number of occlusal contacts per subject in Class I malocclusion was 43. 38 and 44.38 for Class II division 1 malocclusion, this difference was not statistically significant. The occlusal contacts types and frequency in maximum intercuspidation for Class I malocclusion was: cuspid-fossa (32%) (3% tripodism, 14% bipodism, 15% monopodism), cuspid to marginal ridge (21%), cuspid to two marginal ridges (14%), cuspid to inclined plane (11%), surface to surface (22%) and top to top (1%). And in Class II division 1: cuspid-fossa (34%) (4% tripodism, 11% bipodism, 19% monopodism), cuspid to marginal ridge (14%), cuspid to two marginal ridges (13%), cuspid to inclined plane (10%), surface to surface (30%) and top to top (0.4%). There is a variety of factors that influence the number of occlusal contacts. Concluding that there is no occlusal contact type pattern according with the studied malocclusions. A proper selection of occlusal contacts types such as cuspid to fossa or cuspid to marginal ridge and its location in the teeth, should be individually subject defined. The existence of an adequate occlusal contacts, leads to a correct distribution of forces, promoting periodontal health.

Nesta tese, estudamos o problema de Empacotamento de Bicliques. Um biclique é um grafo bipartido completo. No problema de Empacotamento de Bicliques são dados um inteiro k e um grafo bipartido G e deseja-se encontrar um conjunto de k bicliques, subgrafos de G, dois a dois disjuntos nos vértices, tal que a quantidade total de arestas dos bicliques escolhidos seja máxima. No caso em que k=1, temos o problema de Biclique máximo. Esses dois problemas possuem aplicações na área de Bioinformática. Mantemos neste trabalho um enfoque prático, no sentido de que nosso interesse é resolver instâncias desses dois problemas com tamanho razoavelmente grande. Para isso, utilizamos técnicas de Programação Linear Inteira. Para avaliar os métodos propostos aqui, mostramos resultados de experimentos computacionais feitos com instâncias vindas de aplicações e também com instâncias geradas aleatoriamente. / In this thesis, we study the Biclique Packing problem. A biclique is a complete bipartite graph. In the Biclique Packing problem we are given an integer k and a bipartite graph G and we want to find a set of k vertex disjoint bicliques of G, such that the total number of biclique\'s edges is maximum. When k=1, we have the Maximum Biclique problem. These two problems have applications in Bioinformatics. In this work we keep a practical focus, in the sense that we are interested in solving large size instances of these problems. To tackle these problems, we use Integer Linear Programming techniques. In order to evaluate the methods proposed here, we show results of computational experiments carried out with practical application\'s instances and also with randomly generated ones.

Thesis advisor: Christopher Maxwell / In this paper I present an econometric analysis of selection bias in the NBA Draft from 1995-2003. Employing an interval regression maximum likelihood control model that predicts the eventual value of players based on their Draft position, I pinpoint which groups of players consistently over-perform or under-perform relative to their Draft position. Using this analysis I detect bias pertaining to four different groups of players. There was a bias against high school players, especially those taken in the lottery (the top of the first round of the Draft), which may point to risk-averse tendencies of NBA teams. There was also a bias in favor of centers taken in the lottery, who were consistently drafted too high. Black players were selected too low in the first round, and too high in the second round. The final effect deals with foreign entrants to the Draft. From 1995-2001 foreigners were drafted too low; in 2002 and 2003, when more foreigners were selected, they were drafted too high. My paper details the nature of these biases and analyzes their potential causes. / Thesis (BA) — Boston College, 2008. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Economics. / Discipline: Economics Honors Program. / Discipline: College Honors Program.

O avanço da ocupação humana em direção às áreas periurbanas da Região Metropolitana de São Paulo representa sérios riscos aos principais mananciais de abastecimento de água dos municípios da região. A degradação da qualidade destes mananciais pode colocar em risco seu uso preponderante, o que é bastante crítico, visto que a RMSP já apresenta disponibilidade hídrica limitada, o que levou alguns municípios a procurarem formas complementares de abastecimento. O presente trabalho teve como objetivo avaliar o estado trófico e a carga máxima admissível de fósforo do reservatório do Tanque Grande, um manancial superficial do município de Guarulhos, na Grande São Paulo, que é utilizado para abastecimento complementar do município, fornecendo água para cerca de 30.000 habitantes. Apesar de apresentar mais de 90% da área da bacia com cobertura vegetal, poucos habitantes e poucas áreas agrícolas, dados do monitoramento da CETESB indicaram concentrações de fósforo total elevadas, o que motivou a elaboração da pesquisa. Para avaliar o estado trófico do reservatório foram empregadas as metodologias de índice de estado trófico de Lamparelli e o Trophic State Index, além do índice de estado trófico de Carlson, para comparação entre as metodologias. O resultado destes índices subsidiou a análise de carga máxima admissível, cujos resultados foram comparados às estimativas de cargas pontuais e difusas de fósforo produzidas na área da bacia. Foi possível concluir que o reservatório tem apresentado melhora de estado trófico nos últimos anos e que é pouco provável que o processo de eutrofização esteja plenamente estabelecido no reservatório por conta de condições morfométricas, que propiciam boas condições de circulação da massa de água. / The advance of human occupation towards the peri-urban areas of the Metropolitan Region of São Paulo poses serious risks to the main sources of water supply of the regions municipalities. The quality degradation of these sources may endanger its predominant use, which is quite critical since the MRSP already has limited water availability, which led some municipalities to seek additional forms of water supply. This study aimed to evaluate the trophic status and maximum permissible load of phosphorus in the Tanque Grande reservoir, which is used to supplement the water supply of Guarulhos municipality, providing water to approximately 30,000 inhabitants. Despite showing more than 90 % of the basin area with vegetation cover, few residents and few agricultural areas, monitoring data by the CETESB indicated high concentrations of total phosphorus, which motivated the development of the research. To assess the trophic status of the reservoir, the trophic state index of Lamparelli and the trophic state index of Lamparelli, Cunha and Calijuri were employed. The Carlsons trophic state index was also used to compare the methodologies. The result of these indices were used in the maximum permissible load assessment, and the results were compared to estimates of point and non-point loads of phosphorus produced in the basin area. It was concluded that the reservoir has shown improvement in trophic state in recent years and it is unlikely that the process of eutrophication is fully established in the reservoir, probably because of morphometric conditions, which can provide good mixing conditions to the water body.