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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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Submitted on : Friday, October 25, 2019 - 9:51:49 AM
Last modification on : Thursday, October 21, 2021 - 4:06:04 PM
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Karine Bertin, Nicolas Klutchnikoff. Adaptive regression with Brownian path covariate. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2021, 57 (3), pp.1495-1520. ⟨10.1214/20-AIHP1128⟩. ⟨hal-02332820⟩

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