Statistical inference in compound functional models

Abstract : We consider a general nonparametric 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.
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Contributeur : Arnak Dalalyan <>
Soumis le : mercredi 2 janvier 2013 - 15:17:57
Dernière modification le : jeudi 27 avril 2017 - 09:46:25
Document(s) archivé(s) le : mercredi 3 avril 2013 - 03:48:23


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  • HAL Id : hal-00725663, version 3
  • ARXIV : 1208.6402



Arnak S. Dalalyan, Yuri Ingster, Alexandre Tsybakov. Statistical inference in compound functional models. 2012. <hal-00725663v3>



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