Statistical Inference in Compound Functional Models

• Activity Number: 325
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Alexandre Tsybakov*+
• Companies: CREST-ENSAE
• Keywords: compound model ; nonparametric regression ; sparse linear model ; additive model ; minimax rate of convergence ; adaptive estimation

Abstract

This talk deals with a general regression model called the compound model. It includes as special cases sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant covariates. The compound model is characterized by three main parameters: the structure parameter describing the "macroscopic" form of the compound function, the "microscopic" sparsity parameter indicating the maximal number of relevant covariates in each component and the usual smoothness parameter corresponding to the complexity of the members of the compound. We find non-asymptotic minimax rate of convergence of estimators in such a model as a function of these three parameters. We also show that this rate can be attained in an adaptive way. The estimators we consider are based on exponential weighting schemes, and we suggest numerical techniques to approximate them. This is a joint work with Arnak Dalalyan and Yuri Ingster.