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Sparse single-index model
Pierre Alquier1, 2, Gérard Biau1, 3, 4

The single-index model is known to offer a flexible way to model a variety of high-dimensional real-world phenomena. However, despite its relative implicity, this dimension reduction scheme is faced with severe complications as soon as the underlying dimension becomes larger than the number of observations (``p larger than n'' paradigm). To circumvent this difficulty, we consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesian approach. On the theoretical side, we offer a sharp oracle inequality, which is more powerful than the best known oracle inequality for other common procedures of single-index recovery. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technique and its performance is compared with that of standard procedures.
1 :  LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 :  CREST - Centre de Recherche en Économie et Statistique
3 :  LSTA - Laboratoire de Statistique Théorique et Appliquée
4 :  DMA - Département de Mathématiques et Applications
Nonparametric statistics – single-index model – sparsity – PAC-Bayesian inequalities – oracle inequalities – MCMC.