Adaptive regression with Brownian path covariate

07/25/2019

∙

by   Karine Bertin, et al.

∙

0

∙

share

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.