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

TL;DR

This paper develops a robust, adaptive nonparametric estimation method for continuous-time regression models with semi-Markov noise, observed discretely, providing sharp risk bounds and conditions for efficiency.

Contribution

It introduces a novel adaptive model selection procedure with non-asymptotic oracle inequalities for semi-Markov noise models in continuous-time regression.

Findings

Robust minimax convergence rate can vary compared to classical models.

Established conditions for robust efficiency in semi-Markov models.

Provided sharp non-asymptotic risk bounds for the proposed estimator.

Abstract

In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp non-asymptotic oracle inequality for the robust risks is obtained. We obtain sufficient conditions on the frequency observations under which the robust efficiency is shown. It turns out that for the semi-Markov models the robust minimax convergence rate may be faster or slower than the classical one.