Geodesic
Nonparametric estimation in a semimartingale regression model. Part~2. Robust asymptotic efficiency
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 31-45

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In this paper we prove the asymptotic efficiency of the model selection procedure proposed by the authors in [1]. To this end we introduce the robust risk as the least upper bound of the quadratical risk over a broad class of observation distributions. Asymptotic upper and lower bounds for the robust risk have been derived. The asymptotic efficiency of the procedure is proved. The Pinsker constant is found.
Keywords: Non-parametric regression; Model selection; Sharp oracle inequality; Robust risk; Asymptotic efficiency; Pinsker constant; Semimartingale noise. 
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     author = {V. V. Konev and S. M. Pergamenshchikov},
     title = {Nonparametric estimation in a semimartingale regression model. {Part~2.} {Robust} asymptotic efficiency},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {31--45},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/VTGU_2009_4_a2/}
}
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V. V. Konev; S. M. Pergamenshchikov. Nonparametric estimation in a semimartingale regression model. Part~2. Robust asymptotic efficiency. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 31-45. http://geodesic.mathdoc.fr/item/VTGU_2009_4_a2/