As doenças cardiovasculares (DCV) representam a principal causa de mortalidade e de incapacidade, em ambos os gêneros, no Brasil e no mundo. O padrão de consumo alimentar está tanto positiva como negativamente associado aos principais fatores de risco para DCV, entre eles diabetes, hipertensão, obesidade e hipertrigliceridemia, todos componentes da síndrome metabólica. Este estudo tem como objetivos identificar os padrões alimentares em indivíduos com DCV, considerando a densidade de energia, a gordura saturada, a fibra, o sódio e o potássio consumidos, e investigar sua associação com fatores de risco de DCV e síndrome metabólica. Trata-se de um estudo transversal. Foram utilizados dados do estudo DICA Br. A amostra foi composta de indivíduos com DCV, com idade superior a 45 anos, de todas as regiões brasileiras. O consumo alimentar foi obtido por recordatório alimentar de 24h e os padrões alimentares obtidos pela regressão por posto reduzido (RPR). Para a RPR, utilizaram-se 28 grupos alimentares como preditores e como variáveis respostas componentes dietéticos. O teste de Mann Whitney foi utilizado para testar as diferenças entre as médias dos escores. Foram obtidos dados de 1.047 participantes; 95% apresentavam doença arterial coronariana; em sua maioria, eram idosos, da classe econômica C1 e C2 e estudaram até o ensino médio. A prevalência de síndrome metabólica foi de 58%. Foram extraídos dois padrões alimentares. O primeiro foi marcado pelo maior consumo de fibra alimentar e potássio, composto por arroz e feijão, frutas e sucos naturais com ou sem açúcar, legumes, carne bovina ou processada, verduras, raízes e tubérculos. O segundo padrão caracterizou-se pelo consumo de gordura saturada e maior densidade energética, representado por panificados salgados, gorduras, carne bovina e processada, doces caseiros, pizza, salgadinhos de pacote ou festa, sanduíche e alimento salgado pronto para consumo. Houve associação significativa entre o padrão alimentar 1 com medida da circunferência da cintura e nível de HDL adequados e com o padrão 2 e HDL adequado. A adoção do padrão alimentar 1 pode estar associada à proteção contra alguns dos componentes da síndrome metabólica. / Cardiovascular diseases (CVD) are the leading cause of mortality and disability in both genders in Brazil and worldwide. The dietary pattern is at the same time positive and negatively associated with the main risk factors for CVD, including diabetes, hypertension, obesity and hypertriglyceridemia, all components of the metabolic syndrome. This study aims to identify dietary patterns in individuals with CVD, considering the energy density, and the amount of saturated fatty acid, fiber, sodium and potassium of the diet, and to investigate its association with CVD risk factors and metabolic syndrome. This is a cross-sectional study, data were used from \"DICA Br\" study. The sample consisted of individuals with CVD, over 45 years old, residents from all Brazilian regions. Food consumption was obtained by one 24-hours diet recall and dietary patterns by reduced rank regression (RRR). In the RRR, 28 food groups were included as predictors and dietary components was chosen as the response variable. The Mann-Whitney test was used to test the differences between the factors scores\' means. Data of 1047 participants were analyzed. 95% have coronary artery disease, most are elderly, economical class most observed are C1 and C2. Also, most of them and studied up to high school. The prevalence of metabolic syndrome was 58%. Two dietary patterns were extracted: the first one is higher in dietary fiber and potassium, which is composed by rice, beans, fruits and natural juices with or without sugar, vegetables, beef or processed meat, roots and tubers. The second pattern is higher in saturated fatty acid and energy density, represented by breads, fats, and processed meat, homemade pastries, pizza, snacks or party package, sandwich and salty food ready for consumption. There was a significant association between dietary pattern 1 and low waist circumference and adequate high density cholesterol blood concentration. There was a significant association between dietary pattern 2 and adequate high density cholesterol blood concentration. We suggest that the adoption of the dietary pattern 1 may be associated with protection against some of the components of metabolic syndrome.

Made available in DSpace on 2014-06-11T19:32:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-26Bitstream added on 2014-06-13T20:03:29Z : No. of bitstreams: 1 bignardi_ab_dr_jabo.pdf: 1324029 bytes, checksum: eefcd7697892e45dbbe5b9ff67fbe3ce (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Parâmetros genéticos para a produção de leite no dia do controle (PLDC) de primeiras lactações de vacas da raça Holandesa foram estimados utilizando os modelos multicaracterísticas e modelos de regressão aleatória (MRA). Para os modelos multicaracterísticas foram analisados 15.896 controles mensais de produção de leite de 1.820 primeiras lactações de vacas da raça Holandesa. As análises foram realizadas por meio de sete modelos: multicaracterísticas padrão, três modelos de posto reduzido ajustando os primeiros 2,3 e 4 componentes principais genéticos e três modelos utilizando análise de fatores com 2,3 e 4 fatores. Para todos os modelos foram considerados os efeitos aleatórios genético aditivo e residual, e os efeitos sistemáticos do grupo de contemporâneo e da idade da vaca ao parto (efeito linear e quadrática) e do número de dias em lactação (efeito linear). A matriz de (co)variâncias residual, para todos os modelos, foi assumida ter posto completo. Os resultados indicam que somente dois componentes principais são requeridos para modelar a estrutura de (co)variâncias genéticas entre as produções de leite no dia do controle. Além disso, o modelo de posto reduzido diminui consideravelmente o número de parâmetros, sem reduzir a qualidade de ajuste. Para os MRA foram analisados 152.145 controles semanais de produção de leite de 7.317 primeiras lactações de vacas da raça Holandesa, provenientes de rebanhos da região Sudeste do Brasil. As produções de leite no dia do controle (PLDC) foram consideradas em 44 classes semanais de dia em lactação. Os grupos de contemporâneos foram definidos como rebanho-ano-semana do controle compondo 2.539 classes e, contendo, no mínimo, seis animais. O modelo utilizado incluiu os efeitos aleatórios genético aditivo direto, de ambiente permanente e o residual. Foram considerados como efeitos fixos, o grupo de... / Genetic parameters for first lactation test-day milk yields of Holstein cattle were estimated using multivariate and random regression models (RRM). For multivariate model a total of 15,896 individual monthly test-day milk yields (10 test-days), from 1,820 complete first lactations of Holstein cattle. A standard multivariate analysis, reduced rank analyses fitting the first 2, 3 and 4 genetic principal components, and analyses that fitted a factor analytic structure considering 2, 3 and 4 factors, were carried out. All models included also fixed effects of the contemporary groups, age of cow (linear and quadratic effects) and days in milk (linear effect). The residual covariance matrix was assumed to have full rank throughout. The results indicate that only two principal components are required to model the genetic covariance structure among the test-days milk yield. Furthermore, reduced rank model allows decreasing the number of parameter without reducing the goodness of fit considerably. For RRM A total of 152,145 weekly test-day milk yield records from 7,317 first lactations of Holstein cows distributed across 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of days in milk (DIM). The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM, and additive genetic and permanent environmental effects were estimated using B-splines. Residual variances were modeled by step function with 6 variance classes. Although all the model selection criteria utilized indicated the model employing cubic B-splines to both random effects, with 6 knots, a more parsimonious model ... (Complete abstract click electronic access below)

Resumo: Parâmetros genéticos para a produção de leite no dia do controle (PLDC) de primeiras lactações de vacas da raça Holandesa foram estimados utilizando os modelos multicaracterísticas e modelos de regressão aleatória (MRA). Para os modelos multicaracterísticas foram analisados 15.896 controles mensais de produção de leite de 1.820 primeiras lactações de vacas da raça Holandesa. As análises foram realizadas por meio de sete modelos: multicaracterísticas padrão, três modelos de posto reduzido ajustando os primeiros 2,3 e 4 componentes principais genéticos e três modelos utilizando análise de fatores com 2,3 e 4 fatores. Para todos os modelos foram considerados os efeitos aleatórios genético aditivo e residual, e os efeitos sistemáticos do grupo de contemporâneo e da idade da vaca ao parto (efeito linear e quadrática) e do número de dias em lactação (efeito linear). A matriz de (co)variâncias residual, para todos os modelos, foi assumida ter posto completo. Os resultados indicam que somente dois componentes principais são requeridos para modelar a estrutura de (co)variâncias genéticas entre as produções de leite no dia do controle. Além disso, o modelo de posto reduzido diminui consideravelmente o número de parâmetros, sem reduzir a qualidade de ajuste. Para os MRA foram analisados 152.145 controles semanais de produção de leite de 7.317 primeiras lactações de vacas da raça Holandesa, provenientes de rebanhos da região Sudeste do Brasil. As produções de leite no dia do controle (PLDC) foram consideradas em 44 classes semanais de dia em lactação. Os grupos de contemporâneos foram definidos como rebanho-ano-semana do controle compondo 2.539 classes e, contendo, no mínimo, seis animais. O modelo utilizado incluiu os efeitos aleatórios genético aditivo direto, de ambiente permanente e o residual. Foram considerados como efeitos fixos, o grupo de ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Genetic parameters for first lactation test-day milk yields of Holstein cattle were estimated using multivariate and random regression models (RRM). For multivariate model a total of 15,896 individual monthly test-day milk yields (10 test-days), from 1,820 complete first lactations of Holstein cattle. A standard multivariate analysis, reduced rank analyses fitting the first 2, 3 and 4 genetic principal components, and analyses that fitted a factor analytic structure considering 2, 3 and 4 factors, were carried out. All models included also fixed effects of the contemporary groups, age of cow (linear and quadratic effects) and days in milk (linear effect). The residual covariance matrix was assumed to have full rank throughout. The results indicate that only two principal components are required to model the genetic covariance structure among the test-days milk yield. Furthermore, reduced rank model allows decreasing the number of parameter without reducing the goodness of fit considerably. For RRM A total of 152,145 weekly test-day milk yield records from 7,317 first lactations of Holstein cows distributed across 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of days in milk (DIM). The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM, and additive genetic and permanent environmental effects were estimated using B-splines. Residual variances were modeled by step function with 6 variance classes. Although all the model selection criteria utilized indicated the model employing cubic B-splines to both random effects, with 6 knots, a more parsimonious model ... (Complete abstract click electronic access below) / Orientador: Lucia Galvão de Albuquerque / Coorientador: Lenira El Faro Zadra / Coorientador: Roberto Augusto de Almeida Torres Júnior / Banca: Fabyano Fonseca e Silva / Banca: Maria Eugênia Zerlotti Mercadante / Banca: Humberto Tonhati / Banca: Henrique Nunes de Oliveira / Doutor

As doenças cardiovasculares (DCV) representam a principal causa de mortalidade e de incapacidade, em ambos os gêneros, no Brasil e no mundo. O padrão de consumo alimentar está tanto positiva como negativamente associado aos principais fatores de risco para DCV, entre eles diabetes, hipertensão, obesidade e hipertrigliceridemia, todos componentes da síndrome metabólica. Este estudo tem como objetivos identificar os padrões alimentares em indivíduos com DCV, considerando a densidade de energia, a gordura saturada, a fibra, o sódio e o potássio consumidos, e investigar sua associação com fatores de risco de DCV e síndrome metabólica. Trata-se de um estudo transversal. Foram utilizados dados do estudo DICA Br. A amostra foi composta de indivíduos com DCV, com idade superior a 45 anos, de todas as regiões brasileiras. O consumo alimentar foi obtido por recordatório alimentar de 24h e os padrões alimentares obtidos pela regressão por posto reduzido (RPR). Para a RPR, utilizaram-se 28 grupos alimentares como preditores e como variáveis respostas componentes dietéticos. O teste de Mann Whitney foi utilizado para testar as diferenças entre as médias dos escores. Foram obtidos dados de 1.047 participantes; 95% apresentavam doença arterial coronariana; em sua maioria, eram idosos, da classe econômica C1 e C2 e estudaram até o ensino médio. A prevalência de síndrome metabólica foi de 58%. Foram extraídos dois padrões alimentares. O primeiro foi marcado pelo maior consumo de fibra alimentar e potássio, composto por arroz e feijão, frutas e sucos naturais com ou sem açúcar, legumes, carne bovina ou processada, verduras, raízes e tubérculos. O segundo padrão caracterizou-se pelo consumo de gordura saturada e maior densidade energética, representado por panificados salgados, gorduras, carne bovina e processada, doces caseiros, pizza, salgadinhos de pacote ou festa, sanduíche e alimento salgado pronto para consumo. Houve associação significativa entre o padrão alimentar 1 com medida da circunferência da cintura e nível de HDL adequados e com o padrão 2 e HDL adequado. A adoção do padrão alimentar 1 pode estar associada à proteção contra alguns dos componentes da síndrome metabólica. / Cardiovascular diseases (CVD) are the leading cause of mortality and disability in both genders in Brazil and worldwide. The dietary pattern is at the same time positive and negatively associated with the main risk factors for CVD, including diabetes, hypertension, obesity and hypertriglyceridemia, all components of the metabolic syndrome. This study aims to identify dietary patterns in individuals with CVD, considering the energy density, and the amount of saturated fatty acid, fiber, sodium and potassium of the diet, and to investigate its association with CVD risk factors and metabolic syndrome. This is a cross-sectional study, data were used from \"DICA Br\" study. The sample consisted of individuals with CVD, over 45 years old, residents from all Brazilian regions. Food consumption was obtained by one 24-hours diet recall and dietary patterns by reduced rank regression (RRR). In the RRR, 28 food groups were included as predictors and dietary components was chosen as the response variable. The Mann-Whitney test was used to test the differences between the factors scores\' means. Data of 1047 participants were analyzed. 95% have coronary artery disease, most are elderly, economical class most observed are C1 and C2. Also, most of them and studied up to high school. The prevalence of metabolic syndrome was 58%. Two dietary patterns were extracted: the first one is higher in dietary fiber and potassium, which is composed by rice, beans, fruits and natural juices with or without sugar, vegetables, beef or processed meat, roots and tubers. The second pattern is higher in saturated fatty acid and energy density, represented by breads, fats, and processed meat, homemade pastries, pizza, snacks or party package, sandwich and salty food ready for consumption. There was a significant association between dietary pattern 1 and low waist circumference and adequate high density cholesterol blood concentration. There was a significant association between dietary pattern 2 and adequate high density cholesterol blood concentration. We suggest that the adoption of the dietary pattern 1 may be associated with protection against some of the components of metabolic syndrome.

Implementation of the Clean Water Act requires agencies to monitor aquatic sites on a regular basis and evaluate the quality of these sites. Sites are evaluated individually even though there may be numerous sites within a watershed. In some cases, sampling frequency is inadequate and the evaluation of site quality may have low reliability. This dissertation evaluates testing procedures for determination of site quality based on modelbased procedures that allow for other sites to contribute information to the data from the test site. Test procedures are described for situations that involve multiple measurements from sites within a region and single measurements when stressor information is available or when covariates are used to account for individual site differences. Tests based on analysis of variance methods are described for fixed effects and random effects models. The proposed model-based tests compare limits (tolerance limits or prediction limits) for the data with the known standard. When the sample size for the test site is small, using model-based tests improves the detection of impaired sites. The effects of sample size, heterogeneity of variance, and similarity between sites are discussed. Reference-based standards and corresponding evaluation of site quality are also considered. Regression-based tests provide methods for incorporating information from other sites when there is information on stressors or covariates. Extension of some of the methods to multivariate biological observations and stressors is also discussed. Redundancy analysis is used as a graphical method for describing the relationship between biological metrics and stressors. A clustering method for finding stressor-response relationships is presented and illustrated using data from the Mid-Atlantic Highlands. Multivariate elliptical and univariate regions for assessment of site quality are discussed. / Ph. D.

Ce manuscrit regroupe différents travaux explorant les interactions entre les tenseurs et l'apprentissage automatique. Le premier chapitre est consacré à l'extension des modèles de séries reconnaissables de chaînes et d'arbres aux graphes. Nous y montrons que les modèles d'automates pondérés de chaînes et d'arbres peuvent être interprétés d'une manière simple et unifiée à l'aide de réseaux de tenseurs, et que cette interprétation s'étend naturellement aux graphes ; nous étudions certaines propriétés de ce modèle et présentons des résultats préliminaires sur leur apprentissage. Le second chapitre porte sur la minimisation approximée d'automates pondérés d'arbres et propose une approche théoriquement fondée à la problématique suivante : étant donné un automate pondéré d'arbres à n états, comment trouver un automate à m<n états calculant une fonction proche de l'originale. Le troisième chapitre traite de la régression de faible rang pour sorties à structure tensorielle. Nous y proposons un algorithme d'apprentissage rapide et efficace pour traiter un problème de régression dans lequel les sorties des tenseurs. Nous montrons que l'algorithme proposé est un algorithme d'approximation pour ce problème NP-difficile et nous donnons une analyse théorique de ses propriétés statistiques et de généralisation. Enfin, le quatrième chapitre introduit le modèle de mélanges algébriques de distributions. Ce modèle considère des combinaisons affines de distributions (où les coefficients somment à un mais ne sont pas nécessairement positifs). Nous proposons une approche pour l'apprentissage de mélanges algébriques qui étend la méthode tensorielle des moments introduite récemment. . / This thesis tackles several problems exploring connections between tensors and machine learning. In the first chapter, we propose an extension of the classical notion of recognizable function on strings and trees to graphs. We first show that the computations of weighted automata on strings and trees can be interpreted in a natural and unifying way using tensor networks, which naturally leads us to define a computational model on graphs: graph weighted models; we then study fundamental properties of this model and present preliminary learning results. The second chapter tackles a model reduction problem for weighted tree automata. We propose a principled approach to the following problem: given a weighted tree automaton with n states, how can we find an automaton with m<n states that is a good approximation of the original one? In the third chapter, we consider a problem of low rank regression for tensor structured outputs. We design a fast and efficient algorithm to address a regression task where the outputs are tensors. We show that this algorithm generalizes the reduced rank regression method and that it offers good approximation, statistical and generalization guarantees. Lastly in the fourth chapter, we introduce the algebraic mixture model. This model considers affine combinations of probability distributions (where the weights sum to one but may be negative). We extend the recently proposed tensor method of moments to algebraic mixtures, which allows us in particular to design a learning algorithm for algebraic mixtures of spherical Gaussian distributions.

Multivariate linear regression methods are widely used statistical tools in data analysis, and were developed when some response variables are studied simultaneously, in which our aim is to study the relationship between predictor variables and response variables through the regression coefficient matrix. The rapid improvements of information technology have brought us a large number of large-scale data, but also brought us great challenges in data processing. When dealing with high dimensional data, the classical least squares estimation is not applicable in multivariate linear regression analysis. In recent years, some approaches have been developed to deal with high-dimensional data problems, among which dimension reduction is one of the main approaches. In some literature, random projection methods were used to reduce dimension in large datasets. In Chapter 2, a new random projection method, with low-rank matrix approximation, is proposed to reduce the dimension of the parameter space in high-dimensional multivariate linear regression model. Some statistical properties of the proposed method are studied and explicit expressions are then derived for the accuracy loss of the method with Gaussian random projection and orthogonal random projection. These expressions are precise rather than being bounds up to constants. In multivariate regression analysis, reduced rank regression is also a dimension reduction method, which has become an important tool for achieving dimension reduction goals due to its simplicity, computational efficiency and good predictive performance. In practical situations, however, the performance of the reduced rank estimator is not satisfactory when the predictor variables are highly correlated or the ratio of signal to noise is small. To overcome this problem, in Chapter 3, we incorporate matrix projections into reduced rank regression method, and then develop reduced rank regression estimators based on random projection and orthogonal projection in high-dimensional multivariate linear regression models. We also propose a consistent estimator of the rank of the coefficient matrix and achieve prediction performance bounds for the proposed estimators based on mean squared errors. Envelope technology is also a popular method in recent years to reduce estimative and predictive variations in multivariate regression, including a class of methods to improve the efficiency without changing the traditional objectives. Variable selection is the process of selecting a subset of relevant features variables for use in model construction. The purpose of using this technology is to avoid the curse of dimensionality, simplify models to make them easier to interpret, shorten training time and reduce overfitting. In Chapter 4, we combine envelope models and a group variable selection method to propose an envelope-based sparse reduced rank regression estimator in high-dimensional multivariate linear regression models, and then establish its consistency, asymptotic normality and oracle property. Tensor data are in frequent use today in a variety of fields in science and engineering. Processing tensor data is a practical but challenging problem. Recently, the prevalence of tensor data has resulted in several envelope tensor versions. In Chapter 5, we incorporate envelope technique into tensor regression analysis and propose a partial tensor envelope model, which leads to a parsimonious version for tensor response regression when some predictors are of special interest, and then consistency and asymptotic normality of the coefficient estimators are proved. The proposed method achieves significant gains in efficiency compared to the standard tensor response regression model in terms of the estimation of the coefficients for the selected predictors. Finally, in Chapter 6, we summarize the work carried out in the thesis, and then suggest some problems of further research interest. / Dissertation / Doctor of Philosophy (PhD)

Dans la modélisation statistique, nous sommes le plus souvent amené à supposer que le phénomène étudié est généré par une structure pouvant s’ajuster aux données observées. Cette structure fait apparaître une partie principale qui représente le mieux possible le phénomène étudié et qui devrait expliquer les données et une partie supposée négligeable appelée erreur ou innovation. Cette structure complexe est communément appelée un modèle, dont la forme peut être plus ou moins complexe. Afin de simplifier la structure, il est souvent supposé qu’elle repose sur un nombre fini de valeurs, appelées paramètres. Basé sur les données, ces paramètres sont estimés avec ce que l’on appelle des estimateurs. La qualité du modèle pour les données à notre disposition est également fonction des estimateurs et de leurs propriétés, par exemple, est-ce que les estimateurs sont raisonnablement proches des valeurs idéales, c’est-à-dire les vraies valeurs. Des questions d’importance portent sur la qualité de l’ajustement d’un modèle aux données, ce qui se fait par l’étude des propriétés probabilistes et statistiques du terme d’erreur. Aussi, l’étude des relations ou l’absence de ces dernières entre les phénomènes sous des hypothèses complexes sont aussi d’intérêt. Des approches possibles pour cerner ce genre de questions consistent dans l’utilisation des tests portemanteaux, dits également tests de diagnostic. La thèse est présentée sous forme de trois projets. Le premier projet est rédigé en langue anglaise. Il s’agit en fait d’un article actuellement soumis dans une revue avec comité de lecture. Dans ce projet, nous étudions le modèle vectoriel à erreurs multiplicatives (vMEM) pour lequel nous utilisons les propriétés des estimateurs des paramètres du modèle selon la méthode des moments généralisés (GMM) afin d’établir la distribution asymptotique des autocovariances résiduelles. Ceci nous permet de proposer des nouveaux tests diagnostiques pour ce type de modèle. Sous l’hypothèse nulle d’adéquation du modèle, nous montrons que la statistique usuelle de Hosking-Ljung-Box converge vers une somme pondérée de lois de khi-carré indépendantes à un degré de liberté. Un test généralisé de Hosking-Ljung-Box est aussi obtenu en comparant la densité spectrale des résidus de l’estimation et celle présumée sous l’hypothèse nulle. Un avantage des tests spectraux est qu’ils nécessitent des estimateurs qui convergent à la vitesse n−1/2 où n est la taille de l’échantillon, et leur utilisation n’est pas restreinte à une technique particulière, comme par exemple la méthode des moments généralisés. Dans le deuxième projet, nous établissons la distribution asymptotique sous l’hypothèse de faible dépendance des covariances croisées de deux processus stationnaires en covariance. La faible dépendance ici est définie en terme de l’effet limité d’une observation donnée sur les observations futures. Nous utilisons la notion de stabilité et le concept de contraction géométrique des moments. Ces conditions sont plus générales que celles de l’invariance des moments conditionnels d’ordre un à quatre utilisée jusque là par plusieurs auteurs. Un test statistique basé sur les covariances croisées et la matrice des variances et covariances de leur distribution asymptotique est alors proposé et sa distribution asymptotique établie. Dans l’implémentation du test, la matrice des variances et covariances des covariances croisées est estimée à l’aide d’une procédure autorégressive vectorielle robuste à l’autocorrélation et à l’hétéroscédasticité. Des simulations sont ensuite effectuées pour étudier les propriétés du test proposé. Dans le troisième projet, nous considérons un modèle périodique multivarié et cointégré. La présence de cointégration entraîne l’existence de combinaisons linéaires périodiquement stationnaires des composantes du processus étudié. Le nombre de ces combinaisons linéaires linéairement indépendantes est appelé rang de cointégration. Une méthode d’estimation en deux étapes est considérée. La première méthode est appelée estimation de plein rang. Dans cette approche, le rang de cointégration est ignoré. La seconde méthode est appelée estimation de rang réduit. Elle tient compte du rang de cointégration. Cette dernière est une approche non linéaire basée sur des itérations dont la valeur initiale est l’estimateur de plein rang. Les propriétés asymptotiques de ces estimateurs sont aussi établies. Afin de vérifier l’adéquation du modèle, des statistiques de test de type portemanteau sont considérées et leurs distributions asymptotiques sont étudiées. Des simulations sont par la suite présentées afin d’illustrer le comportement du test proposé. / In statistical modeling, we assume that the phenomenon of interest is generated by a model that can be fitted to the observed data. The part of the phenomenon not explained by the model is called error or innovation. There are two parts in the model. The main part is supposed to explain the observed data, while the unexplained part which is supposed to be negligible is also called error or innovation. In order to simplify the structures, the model are often assumed to rely on a finite set of parameters. The quality of a model depends also on the parameter estimators and their properties. For example, are the estimators relatively close to the true parameters ? Some questions also address the goodness-of-fit of the model to the observed data. This question is answered by studying the statistical and probabilistic properties of the innovations. On the other hand, it is also of interest to evaluate the presence or the absence of relationships between the observed data. Portmanteau or diagnostic type tests are useful to address such issue. The thesis is presented in the form of three projects. The first project is written in English as a scientific paper. It was recently submitted for publication. In that project, we study the class of vector multiplicative error models (vMEM). We use the properties of the Generalized Method of Moments to derive the asymptotic distribution of sample autocovariance function. This allows us to propose a new test statistic. Under the null hypothesis of adequacy, the asymptotic distributions of the popular Hosking-Ljung-Box (HLB) test statistics are found to converge in distribution to weighted sums of independent chi-squared random variables. A generalized HLB test statistic is motivated by comparing a vector spectral density estimator of the residuals with the spectral density calculated under the null hypothesis. In the second project, we derive the asymptotic distribution under weak dependence of cross covariances of covariance stationary processes. The weak dependence is defined in term of the limited effect of a given information on future observations. This recalls the notion of stability and geometric moment contraction. These conditions of weak dependence defined here are more general than the invariance of conditional moments used by many authors. A test statistic based on cross covariances is proposed and its asymptotic distribution is established. In the elaboration of the test statistics, the covariance matrix of the cross covariances is obtained from a vector autoregressive procedure robust to autocorrelation and heteroskedasticity. Simulations are also carried on to study the properties of the proposed test and also to compare it to existing tests. In the third project, we consider a cointegrated periodic model. Periodic models are present in the domain of meteorology, hydrology and economics. When modelling many processes, it can happen that the processes are just driven by a common trend. This situation leads to spurious regressions when the series are integrated but have some linear combinations that are stationary. This is called cointegration. The number of stationary linear combinations that are linearly independent is called cointegration rank. So, to model the real relationship between the processes, it is necessary to take into account the cointegration rank. In the presence of periodic time series, it is called periodic cointegration. It occurs when time series are periodically integrated but have some linear combinations that are periodically stationary. A two step estimation method is considered. The first step is the full rank estimation method that ignores the cointegration rank. It provides initial estimators to the second step estimation which is the reduced rank estimation. It is non linear and iterative. Asymptotic properties of the estimators are also established. In order to check for model adequacy, portmanteau type tests and their asymptotic distributions are also derived and their asymptotic distribution are studied. Simulation results are also presented to show the behaviour of the proposed test.

Nous nous intéressons, dans cette thèse, à l'étude des méthodes d'extrapolation polynômiales et à l'application de ces méthodes dans l'accélération de méthodes de points fixes pour des problèmes donnés. L'avantage de ces méthodes d'extrapolation est qu'elles utilisent uniquement une suite de vecteurs qui n'est pas forcément convergente, ou qui converge très lentement pour créer une nouvelle suite pouvant admettreune convergence quadratique. Le développement de méthodes cycliques permet, deplus, de limiter le coût de calculs et de stockage. Nous appliquons ces méthodes à la résolution des équations de Navier-Stokes stationnaires et incompressibles, à la résolution de la formulation Kohn-Sham de l'équation de Schrödinger et à la résolution d'équations elliptiques utilisant des méthodes multigrilles. Dans tous les cas, l'efficacité des méthodes d'extrapolation a été montrée.Nous montrons que lorsqu'elles sont appliquées à la résolution de systèmes linéaires, les méthodes d'extrapolation sont comparables aux méthodes de sous espaces de Krylov. En particulier, nous montrons l'équivalence entre la méthode MMPE et CMRH. Nous nous intéressons enfin, à la parallélisation de la méthode CMRH sur des processeurs à mémoire distribuée et à la recherche de préconditionneurs efficaces pour cette même méthode. / In this thesis, we study polynomial extrapolation methods. We discuss the design and implementation of these methods for computing solutions of fixed point methods. Extrapolation methods transform the original sequance into another sequence that converges to the same limit faster than the original one without having explicit knowledge of the sequence generator. Restarted methods permit to keep the storage requirement and the average of computational cost low. We apply these methods for computing steady state solutions of incompressible flow problems modelled by the Navier-Stokes equations, for solving the Schrödinger equation using the Kohn-Sham formulation and for solving elliptic equations using multigrid methods. In all cases, vector extrapolation methods have a useful role to play. We show that, when applied to linearly generated vector sequences, extrapolation methods are related to Krylov subspace methods. For example, we show that the MMPE approach is mathematically equivalent to CMRH method. We present an implementation of the CMRH iterative method suitable for parallel architectures with distributed memory. Finally, we present a preconditioned CMRH method.

As IC technologies scale to the nanometer regime, efficient and accurate modeling and analysis of VLSI systems with billions of transistors and interconnects becomes increasingly critical and difficult. VLSI systems impacted by the increasingly high dimensional process-voltage-temperature (PVT) variations demand much more modeling and analysis efforts than ever before, while the analysis of large scale on-chip interconnects that requires solving tens of millions of unknowns imposes great challenges in computer aided design areas. This dissertation presents new methodologies for addressing the above two important challenging issues for large scale on-chip interconnect modeling and analysis: In the past, the standard statistical circuit modeling techniques usually employ principal component analysis (PCA) and its variants to reduce the parameter dimensionality. Although widely adopted, these techniques can be very limited since parameter dimension reduction is achieved by merely considering the statistical distributions of the controlling parameters but neglecting the important correspondence between these parameters and the circuit performances (responses) under modeling. This dissertation presents a variety of performance-oriented parameter dimension reduction methods that can lead to more than one order of magnitude parameter reduction for a variety of VLSI circuit modeling and analysis problems. The sheer size of present day power/ground distribution networks makes their analysis and verification tasks extremely runtime and memory inefficient, and at the same time, limits the extent to which these networks can be optimized. Given today?s commodity graphics processing units (GPUs) that can deliver more than 500 GFlops (Flops: floating point operations per second). computing power and 100GB/s memory bandwidth, which are more than 10X greater than offered by modern day general-purpose quad-core microprocessors, it is very desirable to convert the impressive GPU computing power to usable design automation tools for VLSI verification. In this dissertation, for the first time, we show how to exploit recent massively parallel single-instruction multiple-thread (SIMT) based graphics processing unit (GPU) platforms to tackle power grid analysis with very promising performance. Our GPU based network analyzer is capable of solving tens of millions of power grid nodes in just a few seconds. Additionally, with the above GPU based simulation framework, more challenging three-dimensional full-chip thermal analysis can be solved in a much more efficient way than ever before.