Adaptive regression with Brownian path covariate

Abstract : This paper deals with estimation with functional covariates. More precisely , we aim at estimating the regression function m of a continuous outcome Y against a standard Wiener coprocess W. Following Cadre and Truquet (2015) and Cadre, Klutchnikoff, and Massiot (2017) the Wiener-Itô decomposition of m(W) is used to construct a family of estimators. The minimax rate of convergence over specific smoothness classes is obtained. A data-driven selection procedure is defined following the ideas developed by Goldenshluger and Lepski (2011). An oracle-type inequality is obtained which leads to adaptive results.
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https://hal.univ-rennes2.fr/hal-02332820
Contributor : Nicolas Klutchnikoff <>
Submitted on : Friday, October 25, 2019 - 9:51:49 AM
Last modification on : Wednesday, October 30, 2019 - 1:19:12 AM

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  • HAL Id : hal-02332820, version 1
  • ARXIV : 1907.11284

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Karine Bertin, Nicolas Klutchnikoff. Adaptive regression with Brownian path covariate. 2019. ⟨hal-02332820⟩

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