A MINIMAXITY CRITERION IN NONPARAMETRIC REGRESSION-BASED ON LARGE-DEVIATIONS PROBABILITIES

Authors
KOROSTELEV A
Citation
A. Korostelev, A MINIMAXITY CRITERION IN NONPARAMETRIC REGRESSION-BASED ON LARGE-DEVIATIONS PROBABILITIES, Annals of statistics, 24(3), 1996, pp. 1075-1083
Citations number
9
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of statistics → ACNP
ISSN journal
00905364
Volume
24
Issue
3
Year of publication
1996
Pages
1075 - 1083
Database
ISI
SICI code
0090-5364(1996)24:3<1075:AMCINR>2.0.ZU;2-V
Abstract
A large-deviations criterion is proposed for optimality of nonparametr ic regression estimators. The criterion is one of minimaxity of the la rge-deviations probabilities. We study the case where the underlying c lass of regression functions is either Lipschitz or Holder, and when t he loss function involves estimation at a point or in supremum norm. E xact minimax asymptotics are found in the Gaussian case.