DeepAI AI Chat
Log In Sign Up

Adaptive regression with Brownian path covariate

by   Karine Bertin, et al.
Université Rennes 2
Universidad de Valparaíso

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.


page 1

page 2

page 3

page 4


Adaptive Density Estimation on Bounded Domains

We study the estimation, in Lp-norm, of density functions defined on [0,...

On Undersmoothing and Sample Splitting for Estimating a Doubly Robust Functional

We consider the problem of constructing minimax rate-optimal estimators ...

A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

We suppose that a Lévy process is observed at discrete time points. Star...

Avoid Estimating the Unknown Function in a Semiparametric Nonignorable Propensity Model

We study the problem of estimating a functional or a parameter in the co...

Adaptive nonparametric estimation in the functional linear model with functional output

In this paper, we consider a functional linear regression model, where b...

Robust adaptive efficient estimation for a semi-Markov continuous time regression from discrete data

In this article we consider the nonparametric robust estimation problem ...

Adaptive warped kernel estimation for nonparametric regression with circular responses

In this paper, we deal with nonparametric regression for circular data, ...