Adaptive regression with Brownian path covariate
Statistics Theory
2020-11-23 v2 Statistics Theory
Abstract
This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function of a continuous outcome against a standard Wiener coprocess . Following Cadre and Truquet (2015) and Cadre, Klutchnikoff, and Massiot (2017) the Wiener-It\^o decomposition of 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.
Cite
@article{arxiv.1907.11284,
title = {Adaptive regression with Brownian path covariate},
author = {Karine Bertin and Nicolas Klutchnikoff},
journal= {arXiv preprint arXiv:1907.11284},
year = {2020}
}