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Why minimax is not that pessimistic∗

Published online by Cambridge University Press:  03 June 2013

Aurelia Fraysse
Aurelia Fraysse*
Affiliation:
L2S, SUPELEC, CNRS, University Paris-Sud, 3 rue Joliot-Curie, 91190 Gif-Sur-Yvette, France. fraysse@lss.supelec.fr

Abstract

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In nonparametric statistics a classical optimality criterion for estimation procedures isprovided by the minimax rate of convergence. However this point of view can be subject tocontroversy as it requires to look for the worst behavior of an estimation procedure in agiven space. The purpose of this paper is to introduce a new criterion based on genericbehavior of estimators. We are here interested in the rate of convergence obtained withsome classical estimators on almost every, in the sense of prevalence, function in a Besovspace. We also show that generic results coincide with minimax ones in these cases.

Keywords

Minimax theorymaxiset theoryBesov spacesprevalencewavelet bases

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 472 - 484
Copyright
© EDP Sciences, SMAI, 2013

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