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.

翻译：本文涉及功能共变体的估计。 更确切地说, 我们的目标是根据标准 Wiener 共同处理W$来估算连续结果的回归函数 $1 美元。 在 Cadre 和 Truquet (2015) 和 Cadre 、 Klutchnikoff 和 Massiot (2017年) 之后, Wiener- It ⁇ o dicomfication $m( W) 用于构建一个测算员大家庭。 具体平滑类的最小趋同率得到了实现。 根据Goldenshluger 和 Lepski (2011年) 形成的想法确定了数据驱动的筛选程序。 获得了导致适应结果的甲骨文型不平等。