When there are a large number of predictors and few observations, building a regression model to explain the behavior of a response variable such as a patient's medical condition is very challenging. This is a "p ≫n " variable selection problem encountered often in modern applied statistics and data mining. Chapter one of this thesis proposes a rigorous procedure which groups predictors into clusters of "highly-correlated" variables, selects a representative from each cluster, and uses a subset of the representatives for regression modeling. The proposed Penalized method based on Representatives (PR) extends the Lasso for the p ≫ n data and highly correlated variables, to build a sparse model practically interpretable and maintain prediction quality. Moreover, we provide the PR-Sequential Grouped Regression (PR-SGR) to make computation of the PR procedure efficient. Simulation studies show the proposed method outperforms existing methods such as the Lasso/Lars. A real-life example from a mental health diagnosis illustrates the applicability of the PR-SGR. In the second part of the thesis, we study the analysis of time-to-event data called a gap data when missing time intervals (gaps) possibly happen prior to the first observed event time. If a gap occurs prior to the first observed event, then the first observed event may or may not be the first true event. This incomplete knowledge makes the gap data different from the well-studied regular interval censored data. We propose a Non-Parametric Estimate for the Gap data (NPEG) to estimate the survival function for the first true event time, derive its analytic properties and demonstrate its performance in simulations. We also extend the Imputed Empirical Estimating method (IEE), which is an existing nonparametric method for the gap data up to one gap, to handle the gap data with multiple gaps.

L'électricité ne se stockant pas aisément, EDF a besoin d'outils de prévision de consommation et de production efficaces. Le développement de nouvelles méthodes automatiques de sélection et d'estimation de modèles de prévision est nécessaire. En effet, grâce au développement de nouvelles technologies, EDF peut étudier les mailles locales du réseau électrique, ce qui amène à un nombre important de séries chronologiques à étudier. De plus, avec les changements d'habitude de consommation et la crise économique, la consommation électrique en France évolue. Pour cette prévision, nous adoptons ici une méthode semi-paramétrique à base de modèles additifs. L'objectif de ce travail est de présenter des procédures automatiques de sélection et d'estimation de composantes d'un modèle additif avec des estimateurs en plusieurs étapes. Nous utilisons du Group LASSO, qui est, sous certaines conditions, consistant en sélection, et des P-Splines, qui sont consistantes en estimation. Nos résultats théoriques de consistance en sélection et en estimation sont obtenus sans nécessiter l'hypothèse classique que les normes des composantes non nulles du modèle additif soient bornées par une constante non nulle. En effet, nous autorisons cette norme à pouvoir converger vers 0 à une certaine vitesse. Les procédures sont illustrées sur des applications pratiques de prévision de consommation électrique nationale et locale.Mots-clés: Group LASSO, Estimateurs en plusieurs étapes, Modèle Additif, Prévision de charge électrique, P-Splines, Sélection de variables / French electricity load forecasting encounters major changes since the past decade. These changes are, among others things, due to the opening of electricity market (and economical crisis), which asks development of new automatic time adaptive prediction methods. The advent of innovating technologies also needs the development of some automatic methods, because we have to study thousands or tens of thousands time series. We adopt for time prediction a semi-parametric approach based on additive models. We present an automatic procedure for covariate selection in a additive model. We combine Group LASSO, which is selection consistent, with P-Splines, which are estimation consistent. Our estimation and model selection results are valid without assuming that the norm of each of the true non-zero components is bounded away from zero and need only that the norms of non-zero components converge to zero at a certain rate. Real applications on local and agregate load forecasting are provided.Keywords: Additive Model, Group LASSO, Load Forecasting, Multi-stage estimator, P-Splines, Variables selection