Penalized maximum likelihood and semiparametric second-order efficiency

A. S. Dalalyan, G. K. Golubev, A. B. Tsybakov
2006 Annals of Statistics  
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
more » ... rder 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.
doi:10.1214/009053605000000895 fatcat:2yqu4msns5d77jn2worajj66hq