Why minimax is not that pessimistic

Aurelia Fraysse

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 472-484
  • ISSN: 1292-8100

Abstract

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

How to cite

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Fraysse, Aurelia. "Why minimax is not that pessimistic." ESAIM: Probability and Statistics 17 (2013): 472-484. <http://eudml.org/doc/273625>.

@article{Fraysse2013,
abstract = {In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense of prevalence, function in a Besov space. We also show that generic results coincide with minimax ones in these cases.},
author = {Fraysse, Aurelia},
journal = {ESAIM: Probability and Statistics},
keywords = {minimax theory; maxiset theory; Besov spaces; prevalence; wavelet bases},
language = {eng},
pages = {472-484},
publisher = {EDP-Sciences},
title = {Why minimax is not that pessimistic},
url = {http://eudml.org/doc/273625},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Fraysse, Aurelia
TI - Why minimax is not that pessimistic
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 472
EP - 484
AB - In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense of prevalence, function in a Besov space. We also show that generic results coincide with minimax ones in these cases.
LA - eng
KW - minimax theory; maxiset theory; Besov spaces; prevalence; wavelet bases
UR - http://eudml.org/doc/273625
ER -

References

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