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Statistical Inference in Compound Functional Models

Author

Listed:
  • Arnak Dalalyan

    () (CREST)

  • Yuri Ingster

    () (St-Petersburg State Electotechnical University)

  • Alexandre B. Tsybakov

    () (CREST)

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

Suggested Citation

  • Arnak Dalalyan & Yuri Ingster & Alexandre B. Tsybakov, 2012. "Statistical Inference in Compound Functional Models," Working Papers 2012-20, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2012-20
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    Cited by:

    1. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.

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    Keywords

    Compound functional model; Minimax estimation; Sparse additive stucture; Dimension reduction; Structure adaptation;

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