# Efficient robust nonparametric estimation in a semimartingale regression model

Victor Konev; Serguei Pergamenshchikov

Annales de l'I.H.P. Probabilités et statistiques (2012)

- Volume: 48, Issue: 4, page 1217-1244
- ISSN: 0246-0203

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topKonev, Victor, and Pergamenshchikov, Serguei. "Efficient robust nonparametric estimation in a semimartingale regression model." Annales de l'I.H.P. Probabilités et statistiques 48.4 (2012): 1217-1244. <http://eudml.org/doc/272010>.

@article{Konev2012,

abstract = {The paper considers the problem of robust estimating a periodic function in a continuous time regression model with the dependent disturbances given by a general square integrable semimartingale with an unknown distribution. An example of such a noise is a non-Gaussian Ornstein–Uhlenbeck process with jumps (see (J. R. Stat. Soc. Ser. B Stat. Methodol.63 (2001) 167–241), (Ann. Appl. Probab.18 (2008) 879–908)). 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. It is established that, in the case of the non-Gaussian Ornstein–Uhlenbeck noise, the sharp lower bound for the robust quadratic risk is determined by the limit value of the noise intensity at high frequencies. An example with a martinagale noise exhibits that the risk convergence rate becomes worse if the noise intensity is unbounded.},

author = {Konev, Victor, Pergamenshchikov, Serguei},

journal = {Annales de l'I.H.P. Probabilités et statistiques},

keywords = {non-asymptotic estimation; robust risk; model selection; sharp oracle inequality; asymptotic efficiency},

language = {eng},

number = {4},

pages = {1217-1244},

publisher = {Gauthier-Villars},

title = {Efficient robust nonparametric estimation in a semimartingale regression model},

url = {http://eudml.org/doc/272010},

volume = {48},

year = {2012},

}

TY - JOUR

AU - Konev, Victor

AU - Pergamenshchikov, Serguei

TI - Efficient robust nonparametric estimation in a semimartingale regression model

JO - Annales de l'I.H.P. Probabilités et statistiques

PY - 2012

PB - Gauthier-Villars

VL - 48

IS - 4

SP - 1217

EP - 1244

AB - The paper considers the problem of robust estimating a periodic function in a continuous time regression model with the dependent disturbances given by a general square integrable semimartingale with an unknown distribution. An example of such a noise is a non-Gaussian Ornstein–Uhlenbeck process with jumps (see (J. R. Stat. Soc. Ser. B Stat. Methodol.63 (2001) 167–241), (Ann. Appl. Probab.18 (2008) 879–908)). 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. It is established that, in the case of the non-Gaussian Ornstein–Uhlenbeck noise, the sharp lower bound for the robust quadratic risk is determined by the limit value of the noise intensity at high frequencies. An example with a martinagale noise exhibits that the risk convergence rate becomes worse if the noise intensity is unbounded.

LA - eng

KW - non-asymptotic estimation; robust risk; model selection; sharp oracle inequality; asymptotic efficiency

UR - http://eudml.org/doc/272010

ER -

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