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Model selection via testing : an alternative to (penalized) maximum likelihood estimators

Lucien Birgé — 2006

Annales de l'I.H.P. Probabilités et statistiques

Stabilité et instabilité du risque minimax pour des variables indépendantes équidistribuées

Lucien Birge — 1984

Annales de l'I.H.P. Probabilités et statistiques

Sur les vitesses exponentielles de décroissance des erreurs des tests de rapport de vraisemblances

Lucien Birge — 1979

Annales scientifiques de l'Université de Clermont. Mathématiques

Estimating composite functions by model selection

Yannick Baraud; Lucien Birgé — 2014

Annales de l'I.H.P. Probabilités et statistiques

We consider the problem of estimating a function $s$ on ${[- 1, 1]}^{k}$ for large values of $k$ by looking for some best approximation of $s$ by composite functions of the form $g \circ u$ . 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 $g, u$ and statistical frameworks. In particular, we handle the problems of approximating $s$ by additive functions, single and multiple index models, artificial neural networks, mixtures of Gaussian...

Gaussian model selection

Lucien Birgé; Pascal Massart — 2001

Journal of the European Mathematical Society

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

Lucien Birgé; Yves Rozenholc — 2006

ESAIM: Probability and Statistics

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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Currently displaying 1 – 6 of 6

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

Gaussian model selection

How many bins should be put in a regular histogram