Statistical Inference in Compound Functional Models

Arnak Dalalyan, Yuri Ingster () and Alexandre Tsybakov
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Yuri Ingster: St-Petersburg State Electotechnical University

No 2012-20, Working Papers from Center for Research in Economics and Statistics

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

Keywords: Compound functional model; Minimax estimation; Sparse additive stucture; Dimension reduction; Structure adaptation (search for similar items in EconPapers)
Pages: 15
Date: 2012-09
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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