Model selection via testing : an alternative to (penalized) maximum likelihood estimators
Stabilité et instabilité du risque minimax pour des variables indépendantes équidistribuées
Sur les vitesses exponentielles de décroissance des erreurs des tests de rapport de vraisemblances
Estimating composite functions by model selection
We consider the problem of estimating a function on for large values of by looking for some best approximation of by composite functions of the form . Our solution is based on model selection and leads to a very general approach to solve this problem with respect to many different types of functions and statistical frameworks. In particular, we handle the problems of approximating by additive functions, single and multiple index models, artificial neural networks, mixtures of Gaussian...
Gaussian model selection
Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...
How many bins should be put in a regular histogram
Given an -sample from some unknown density on , it is easy to construct an histogram of the data based on some given partition of , but not so much is known about an optimal choice of the partition, especially when the data set is not large, even if one restricts to partitions into intervals of equal length. Existing methods are either rules of thumbs or based on asymptotic considerations and often involve some smoothness properties of . Our purpose in this paper is to give an automatic, easy...
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