Robust adaptive efficient estimation for semi-Markov nonparametric regression models

TL;DR

This paper develops a robust, adaptive estimation method for continuous-time semi-Markov regression models, achieving sharp non-asymptotic risk bounds and revealing that convergence rates can vary from classical expectations.

Contribution

It introduces a novel adaptive model selection procedure for semi-Markov models with robust risk bounds and analyzes the convergence rate behavior.

Findings

Sharp non-asymptotic oracle inequality established

Robust efficiency demonstrated under general noise conditions

Minimax convergence rate can differ from classical rates in semi-Markov models

Abstract

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp non-asymptotic oracle inequality for the robust risks is obtained and the robust efficiency is shown. It turns out that for semi-Markov models the robust minimax convergence rate may be faster or slower than the classical one.