Statistical Inference in Compound Functional Models
AbstractWe 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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Bibliographic InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2012-20.
Date of creation: Sep 2012
Date of revision:
Compound functional model; Minimax estimation; Sparse additive stucture; Dimension reduction; Structure adaptation;
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