2006/02/01 by A. S. Dalalyan, G. K. Golubev, A. B. Tsybakov · 3 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Distributed Sensor Networks and Detection Algorithms #Financial Risk and Volatility Modeling #Statistical Methods and Inference #math.ST #msc:62G05 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/009053605000000895
published as Annals of Statistics 2006, Vol. 34, No. 1, 169-201 · Published at http://dx.doi.org/10.1214/009053605000000895 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2006/02/01 · arxiv created 2006/05/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.