Cette thèse est consacrée à l'étude de certains modèles de déformation semi-paramétriques. Notre objectif est de proposer des méthodes récursives, issues d'algorithmes stochastiques, pour estimer les paramètres de ces modèles. Dans la première partie, on présente les outils théoriques existants qui nous seront utiles dans la deuxième partie. Dans un premier temps, on présente un panorama général sur les méthodes d'approximation stochastique, en se focalisant en particulier sur les algorithmes de Robbins-Monro et de Kiefer-Wolfowitz. Dans un second temps, on présente les méthodes à noyaux pour l'estimation de fonction de densité ou de régression. On s'intéresse plus particulièrement aux deux estimateurs à noyaux les plus courants qui sont l'estimateur de Parzen-Rosenblatt et l'estimateur de Nadaraya-Watson, en présentant les versions récursives de ces deux estimateurs.Dans la seconde partie, on présente tout d'abord une procédure d'estimation récursive semi-paramétrique du paramètre de translation et de la fonction de régression pour le modèle de translation dans la situation où la fonction de lien est périodique. On généralise ensuite ces techniques au modèle vectoriel de déformation à forme commune en estimant les paramètres de moyenne, de translation et d'échelle, ainsi que la fonction de régression. On s'intéresse finalement au modèle de déformation paramétrique de variables aléatoires dans le cadre où la déformation est connue à un paramètre réel près. Pour ces trois modèles, on établit la convergence presque sûre ainsi que la normalité asymptotique des estimateurs paramétriques et non paramétriques proposés. Enfin, on illustre numériquement le comportement de nos estimateurs sur des données simulées et des données réelles. / This thesis is devoted to the study of some semi-parametric deformation models.Our aim is to provide recursive methods, related to stochastic algorithms, in order to estimate the different parameters of the models. In the first part, we present the theoretical tools which we will use in the next part. On the one hand, we focus on stochastic approximation methods, in particular the Robbins-Monro algorithm and the Kiefer-Wolfowitz algorithm. On the other hand, we introduce kernel estimators in order to estimate a probability density function and a regression function. More particularly, we present the two most famous kernel estimators which are the one of Parzen-Rosenblatt and the one of Nadaraya-Watson. We also present their recursive version.In the second part, we present the results we obtained in this thesis.Firstly, we provide a recursive estimation method of the shift parameter and the regression function for the translation model in which the regression function is periodic. Secondly, we extend this estimation procedure to the shape invariant model, providing estimation of the height parameter, the translation parameter and the scale parameter, as well as the common shape function.Thirdly, we are interested in the parametric deformation model of random variables where the deformation is known and depending on an unknown parameter.For these three models, we establish the almost sure convergence and the asymptotic normality of each estimator. Finally, we numerically illustrate the asymptotic behaviour of our estimators on simulated data and on real data.

Este trabalho propõe modelos Bayesiano semi-paramétricos para dados binários. O primeiro modelo é uma mistura em escala que permite lidar com discrepâncias relacionadas a curtose do modelo Logístico. É uma extensão relevante a partir do que já foi proposto por Basu e Mukhopadhyay (2000) ao possibilitar a interpretação da distribuição a priori dos parâmetros através de razões de chances. O segundo modelo usufrui da mistura em escala em conjunto com a transformação proposta por \\Yeo e Johnson (2000) possibilitando que a curtose assim como a assimetria sejam ajustadas e um parâmetro informativo de assimetria seja estimado. Esta transformação é muito mais apropriada para lidar com valores negativos do que a transformação de Box e Cox (1964) utilizada por Guerrero e Johnson (1982) e é mais simples do que o modelo proposto por Stukel (1988). Por fim, o terceiro modelo é o mais geral entre todos e consiste em uma mistura de posição e escala tal que possa descrever curtose, assimetria e também bimodalidade. O modelo proposto por Newton et al. (1996), embora, seja bastante geral, não permite uma interpretação palpável da distribuição a priori para os pesquisadores da área aplicada. A avaliação dos modelos é realizada através de medidas de distância de probabilidade Cramér-von Mises, Kolmogorov-Smirnov e Anderson-Darling e também pelas Ordenadas Preditivas Condicionais. / This work proposes semi-parametric Bayesian models for binary data. The first model is a scale mixture that allows handling discrepancies related to kurtosis of Logistic model. It is a more interesting extension than has been proposed by Basu e Mukhopadyay (1998) because this model allows the interpretation of the prior distribution of parameters using odds ratios. The second model enjoys the scale mixture together with the scale transformation proposed by Yeo and Johnson (2000) modeling the kurtosis and the asymmetry such that a parameter of asymmetry is estimated. This transformation is more appropriate to deal with negative values than the transformation of Box e Cox (1964) used by Guerrero e Johnson (1982) and simpler than the model proposed by Stukel (1988). Finally, the third model is the most general among all and consists of a location-scale mixture that can describe kurtosis and skewness also bimodality. The model proposed by Newton et al (1996), although general, does not allow a tangible interpretation of the a priori distribution for reseachers of applied area. The evaluation of the models is performed through distance measurements of distribution of probabilities Cramer-von Mises Kolmogorov-Smirnov and Anderson-Darling and also the Conditional Predictive sorted.

This paper proposes for the purposes of freight generation a spatial autoregressive model framework, combined with non-linear semi-parametric techniques. We demonstrate the capabilities of the model in a series of Monte Carlo studies. Moreover, evidence is provided for non-linearities in freight generation, through an applied analysis of European NUTS-2 regions. We provide evidence for significant spatial dependence and for significant non-linearities related to employment rates in manufacturing and infrastructure capabilities in regions. The non-linear impacts are the most significant in the agricultural freight generation sector.

No description available.

Dans un contexte de test multiple, nous considérons un modèle de mélange semi-paramétrique avec deux composantes. Une composante est supposée connue et correspond à la distribution des p-valeurs sous hypothèse nulle avec probabilité a priori p. L'autre composante f est nonparamétrique et représente la distribution des p-valeurs sous l'hypothèse alternative. Le problème d'estimer les paramètres p et f du modèle apparaît dans les procédures de contrôle du taux de faux positifs (``false discovery rate'' ou FDR). Dans la première partie de cette dissertation, nous étudions l'estimation de la proportion p. Nous discutons de résultats d'efficacité asymptotique et établissons que deux cas différents arrivent suivant que f s'annule ou non surtout un intervalle non-vide. Dans le premier cas (annulation surtout un intervalle), nous présentons des estimateurs qui convergent \`{a} la vitesse paramétrique, calculons la variance asymptotique optimale et conjecturons qu'aucun estimateur n'est asymptotiquement efficace (i.e atteint la variance asymptotique optimale). Dans le deuxième cas, nous prouvons que le risque quadratique de n'importe quel estimateur ne converge pas à la vitesse paramétrique. Dans la deuxième partie de la dissertation, nous nous concentrons sur l'estimation de la composante inconnue nonparamétrique f dans le mélange, en comptant sur un estimateur préliminaire de p. Nous proposons et étudions les propriétés asymptotiques de deux estimateurs différents pour cette composante inconnue. Le premier estimateur est un estimateur à noyau avec poids aléatoires. Nous établissons une borne supérieure pour son risque quadratique ponctuel, en montrant une vitesse de convergence nonparamétrique classique sur une classe de Holder. Le deuxième estimateur est un estimateur du maximum de vraisemblance régularisée. Il est calculé par un algorithme itératif, pour lequel nous établissons une propriété de décroissance d'un critère. De plus, ces estimateurs sont utilisés dans une procédure de test multiple pour estimer le taux local de faux positifs (``local false discovery rate'' ou lfdr). / In a multiple testing context, we consider a semiparametric mixture model with two components. One component is assumed to be known and corresponds to the distribution of p-values under the null hypothesis with prior probability p. The other component f is nonparametric and stands for the distribution under the alternative hypothesis. The problem of estimating the parameters p and f of the model appears from the false discovery rate control procedures. In the first part of this dissertation, we study the estimation of the proportion p. We discuss asymptotic efficiency results and establish that two different cases occur whether f vanishes on a non-empty interval or not. In the first case, we exhibit estimators converging at parametric rate, compute the optimal asymptotic variance and conjecture that no estimator is asymptotically efficient (i.e. attains the optimal asymptotic variance). In the second case, we prove that the quadratic risk of any estimator does not converge at parametric rate. In the second part of the dissertation, we focus on the estimation of the nonparametric unknown component f in the mixture, relying on a preliminary estimator of p. We propose and study the asymptotic properties of two different estimators for this unknown component. The first estimator is a randomly weighted kernel estimator. We establish an upper bound for its pointwise quadratic risk, exhibiting the classical nonparametric rate of convergence over a class of Holder densities. The second estimator is a maximum smoothed likelihood estimator. It is computed through an iterative algorithm, for which we establish a descent property. In addition, these estimators are used in a multiple testing procedure in order to estimate the local false discovery rate.

Neste trabalho foi proposto o modelo linear parcial generalizado simétrico, com base nos modelos lineares parciais generalizados e nos modelos lineares simétricos, em que a variável resposta segue uma distribuição que pertence à família de distribuições simétricas, considerando um preditor linear que possui uma parte paramétrica e uma não paramétrica. Algumas distribuições que pertencem a essa classe são as distribuições: Normal, t-Student, Exponencial potência, Slash e Hiperbólica, dentre outras. Uma breve revisão dos conceitos utilizados ao longo do trabalho foram apresentados, a saber: análise residual, influência local, parâmetro de suavização, spline, spline cúbico, spline cúbico natural e algoritmo backfitting, dentre outros. Além disso, é apresentada uma breve teoria dos modelos GAMLSS (modelos aditivos generalizados para posição, escala e forma). Os modelos foram ajustados utilizando o pacote gamlss disponível no software livre R. A seleção de modelos foi baseada no critério de Akaike (AIC). Finalmente, uma aplicação é apresentada com base em um conjunto de dados reais da área financeira do Chile. / In this work we propose the symmetric generalized partial linear model, based on the generalized partial linear models and symmetric linear models, that is, the response variable follows a distribution that belongs to the symmetric distribution family, considering a linear predictor that has a parametric and a non-parametric component. Some distributions that belong to this class are distributions: Normal, t-Student, Power Exponential, Slash and Hyperbolic among others. A brief review of the concepts used throughout the work was presented, namely: residual analysis, local influence, smoothing parameter, spline, cubic spline, natural cubic spline and backfitting algorithm, among others. In addition, a brief theory of GAMLSS models is presented (generalized additive models for position, scale and shape). The models were adjusted using the package gamlss available in the free R software. The model selection was based on the Akaike criterion (AIC). Finally, an application is presented based on a set of real data from Chile\'s financial area.

No description available.

Neste trabalho foi proposto o modelo linear parcial generalizado simétrico, com base nos modelos lineares parciais generalizados e nos modelos lineares simétricos, em que a variável resposta segue uma distribuição que pertence à família de distribuições simétricas, considerando um preditor linear que possui uma parte paramétrica e uma não paramétrica. Algumas distribuições que pertencem a essa classe são as distribuições: Normal, t-Student, Exponencial potência, Slash e Hiperbólica, dentre outras. Uma breve revisão dos conceitos utilizados ao longo do trabalho foram apresentados, a saber: análise residual, influência local, parâmetro de suavização, spline, spline cúbico, spline cúbico natural e algoritmo backfitting, dentre outros. Além disso, é apresentada uma breve teoria dos modelos GAMLSS (modelos aditivos generalizados para posição, escala e forma). Os modelos foram ajustados utilizando o pacote gamlss disponível no software livre R. A seleção de modelos foi baseada no critério de Akaike (AIC). Finalmente, uma aplicação é apresentada com base em um conjunto de dados reais da área financeira do Chile. / In this work we propose the symmetric generalized partial linear model, based on the generalized partial linear models and symmetric linear models, that is, the response variable follows a distribution that belongs to the symmetric distribution family, considering a linear predictor that has a parametric and a non-parametric component. Some distributions that belong to this class are distributions: Normal, t-Student, Power Exponential, Slash and Hyperbolic among others. A brief review of the concepts used throughout the work was presented, namely: residual analysis, local influence, smoothing parameter, spline, cubic spline, natural cubic spline and backfitting algorithm, among others. In addition, a brief theory of GAMLSS models is presented (generalized additive models for position, scale and shape). The models were adjusted using the package gamlss available in the free R software. The model selection was based on the Akaike criterion (AIC). Finally, an application is presented based on a set of real data from Chile\'s financial area.

nÃo hà / This article is an analysis of the validity of the hypothesis that states the tendency of common growth presented in the evolution of the prices of 31 of the major financial stock institutions listed on BM&F Bovespa during the period of January 2000 to June 2007, based on the framework of semi-parametric Philips e Sul (2007). Since stocks are derived from the day-to-day of a business, this work seeks to show whether there are actions that converge to a certain level of real cumulative returns and, based on it, analyze what factors they have in common that will comprise each convergence club. The results obtained should add to the literature of share performance in banks and financial companies, by highlighting the existence of four convergence clubs, with their own dynamic transition, whose composition appear to have specific characteristics. The first club owns volatile shares of large institutions with a high payout and ROE, while the other ones can be associated with a reduction in both the financial indicators and other performance indicators such as the Sharpe ratio and Sortino ratio. Even if the first group, made only by multi-banks and the second by private companies it is not enough to designate a pattern from these characteristics, therefore, demystifying the questions related to the efficiency of public banks in comparison to private banks. / Este estudo consiste em uma anÃlise da validade da hipÃtese de tendÃncia de crescimento comum presente na evoluÃÃo da cotaÃÃo de 31 aÃÃes das principais instituiÃÃes financeiras cotadas na BM&FBovespa durante o perÃodo de janeiro de 2000 a junho de 2007, com base no arcabouÃo semi paramÃtrico de Philips e Sul (2007). Sendo as aÃÃes uma derivada do dia-a-dia da empresa, este trabalho busca evidenciar se existem aÃÃes que convergem para determinado nÃvel de retorno real acumulado e diante disso analisar que fatores em comum possuem estas aÃÃes que formam cada clube de convergÃncia. Os resultados obtidos agregam-se à literatura de performance de aÃÃes de bancos e empresas financeiras, ao permitir evidenciar a existÃncia de quatro clubes de convergÃncia, com dinÃmicas de transiÃÃo bastante prÃprias, cuja composiÃÃo parece possuir caracterÃsticas bastante especÃficas. O primeiro clube possui aÃÃes volÃteis de instituiÃÃes de grande porte e de elevado payout e ROE, enquanto nos demais à possÃvel observar uma reduÃÃo tanto dos indicadores financeiros quanto de outros indicadores de performance, tais como Ãndice de Sharpe e Ãndice de Sortino. Em que pese o primeiro grupo ser formado somente por bancos mÃltiplos e o segundo apenas por empresas privadas, nÃo se pode chegar num padrÃo a partir dessas duas caracterÃsticas, desmitificando algumas questÃes relativas à eficiÃncia na gestÃo de bancos pÃblicos em relaÃÃo aos bancos privados.

Les études observationnelles (non-randomisées) sont principalement constituées de données ayant des particularités qui sont en fait contraignantes dans un cadre statistique classique. En effet, dans ce type d'études, les données sont rarement continues, complètes et indépendantes du bras thérapeutique dans lequel les observations se situent. Cette thèse aborde l'utilisation d'un outil statistique paramétrique fondé sur la dépendance entre les données à travers plusieurs scénarios liés aux études observationnelles. En effet, grâce au théorème de Sklar (1959), les copules paramétriques sont devenues un sujet d'actualité en biostatistique. Pour commencer, nous présentons les concepts de base relatifs aux copules et aux principales mesures d'association basées sur la concordance retrouvées dans la littérature. Ensuite, nous donnons trois exemples d'application des modèles de copules paramétriques pour autant de cas de données particulières retrouvées dans des études observationnelles. Nous proposons d’abord une stratégie de modélisation de l'analyse coût-efficacité basée uniquement sur une réécriture des fonctions de distribution jointes et évitant les modèles de régression linéaire. Nous étudions ensuite, les contraintes relatives aux données discrètes, particulièrement dans un contexte de non-unicité de la fonction copule, nous réécrivons le score de propension grâce à une approche novatrice basée sur l'extension d'une sous-copule. Enfin, nous évoquons un type particulier de données manquantes : les données censurées à droite, dans un contexte de régression, grâce à l'utilisation de copules semi-paramétriques. / Observational studies (non-randomized) consist primarily of data with features that are in fact constraining within a classical statistical framework. Indeed, in this type of study, data are rarely continuous, complete, and independent of the therapeutic arm the observations are belonging to. This thesis deals with the use of a parametric statistical tool based on the dependence between the data, using several scenarios related to observational studies. Indeed, thanks to the theorem of Sklar (1959), parametric copulas have become a topic of interest in biostatistics. To begin with, we present the basic concepts of copulas, as well as the main measures of association based on the concordance founded on an analysis of the literature. Then, we give three examples of application of models of parametric copulas for as many cases of specific data found in observational studies. We first propose a strategy of modeling cost-effectiveness analysis based essentially on rewriting the joint distribution functions, while discarding the use of linear regression models. We then study the constraints relative to discrete data, particularly in a context of non-unicity of the copula function. We rewrite the propensity score, thanks to an innovative approach based on the extension of a sub-copula. Finally, we introduce a particular type of missing data: right censored data, in a regression context, through the use of semi-parametric copulas.