Efficient robust nonparametric estimation in a semimartingale regression model

Victor Konev; Serguei Pergamenchtchikov

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arXiv · 1010.3366

Efficient robust nonparametric estimation in a semimartingale regression model

Victor Konev·Serguei Pergamenchtchikov

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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.

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Victor Konev, Serguei Pergamenchtchikov. 2010-10-16. Efficient robust nonparametric estimation in a semimartingale regression model. https://arxiv.org/abs/1010.3366

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