Efficient robust nonparametric estimation in a semimartingale regression model
Statistics Theory
2010-10-20 v1 Statistics Theory
Abstract
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a noise is non-gaussian Ornstein-Uhlenbeck process with the L\'evy process subordinator, which is used to model the financial Black-Scholes type markets with jumps. An adaptive model selection procedure, based on the weighted least square estimates, is proposed. Under general moment conditions on the noise distribution, sharp non-asymptotic oracle inequalities for the robust risks have been derived and the robust efficiency of the model selection procedure has been shown.
Cite
@article{arxiv.1010.3366,
title = {Efficient robust nonparametric estimation in a semimartingale regression model},
author = {Victor Konev and Serguei Pergamenchtchikov},
journal= {arXiv preprint arXiv:1010.3366},
year = {2010}
}