A CONSTRAINED RISK INEQUALITY WITH APPLICATIONS TO NONPARAMETRIC FUNCTIONAL ESTIMATION

Authors
BROWN LD LOW MG
Citation
Ld. Brown et Mg. Low, A CONSTRAINED RISK INEQUALITY WITH APPLICATIONS TO NONPARAMETRIC FUNCTIONAL ESTIMATION, Annals of statistics, 24(6), 1996, pp. 2524-2535
Citations number
24
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of statistics → ACNP
ISSN journal
00905364
Volume
24
Issue
6
Year of publication
1996
Pages
2524 - 2535
Database
ISI
SICI code
0090-5364(1996)24:6<2524:ACRIWA>2.0.ZU;2-D
Abstract
A general constrained minimum risk inequality is derived. Given two de nsities f(theta) and f(0) we find a lower bound for the risk at the po int theta given an upper bound for the risk at the point 0. The inequa lity sheds new light on superefficient estimators in the normal locati on problem and also on an adaptive estimation problem arising in nonpa rametric functional estimation.