Robust adaptive efficient estimation for semi-Markov nonparametric regression models

摘要

We consider the nonparametric robust estimation problem for regression modelsin continuous time with semi-Markov noises. An adaptive model selectionprocedure is proposed. Under general moment conditions on the noisedistribution a sharp non-asymptotic oracle inequality for the robust risks isobtained and the robust efficiency is shown. It turns out that for semi-Markovmodels the robust minimax convergence rate may be faster or slower than theclassical one.