Efficient robust nonparametric estimation in a semimartingale regression model

Victor Konev (1) , Serguei Pergamenchtchikov (2)

1 Université de Tomsk
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

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 Lévy 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.

Mots clés: Non-asymptotic estimation; Robust risk; Model selection; Sharp oracle inequality; Asymptotic efficiency.; Asymptotic efficiency

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Victor Konev, Serguei Pergamenchtchikov. Efficient robust nonparametric estimation in a semimartingale regression model. 2010. ⟨hal-00526915⟩