  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.
