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February 2006 Penalized maximum likelihood and semiparametric second-order efficiency
A. S. Dalalyan, G. K. Golubev, A. B. Tsybakov
Ann. Statist. 34(1): 169-201 (February 2006). DOI: 10.1214/009053605000000895


We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the second-order terms in asymptotic expansion for the risk account for the behavior of the “nonparametric component” of a semiparametric procedure, and they are not dramatically smaller than the first-order terms.


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A. S. Dalalyan. G. K. Golubev. A. B. Tsybakov. "Penalized maximum likelihood and semiparametric second-order efficiency." Ann. Statist. 34 (1) 169 - 201, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

MathSciNet: MR2275239
zbMATH: 1091.62020
Digital Object Identifier: 10.1214/009053605000000895

Primary: 62G05 , 62G20

Keywords: estimating a shift of a nonparametric function , exact minimax asymptotics , penalized maximum likelihood , second-order efficiency , Semiparametric estimation

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2006
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