Penalized maximum likelihood and semiparametric second-order efficiency

Details Penalized maximum likelihood and semiparametric second-order efficiency Penalized maximum likelihood and semiparametric second-order efficiency

2006-05-16

arxiv.org/abs/math/0605437v1

Annals of Statistics 2006, Vol. 34, No. 1, 169-201

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000895 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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