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arXiv · 1907.11284

Adaptive regression with Brownian path covariate

Karine Bertin·Nicolas Klutchnikoff
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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-It\^o 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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Karine Bertin, Nicolas Klutchnikoff. 2019-07-25. Adaptive regression with Brownian path covariate. https://arxiv.org/abs/1907.11284

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