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February 2009 Superefficiency from the Vantage Point of Computability
Vladimir Vovk
Statist. Sci. 24(1): 73-86 (February 2009). DOI: 10.1214/09-STS279

Abstract

In 1952 Lucien Le Cam announced his celebrated result that, for regular univariate statistical models, sets of points of superefficiency have Lebesgue measure zero. After reviewing the turbulent history of early studies of superefficiency, I suggest using the notion of computability as a tool for exploring the phenomenon of superefficiency. It turns out that only computable parameter points can be points of superefficiency for computable estimators. This algorithmic version of Le Cam’s result implies, in particular, that sets of points of superefficiency not only have Lebesgue measure zero but are even countable.

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Vladimir Vovk. "Superefficiency from the Vantage Point of Computability." Statist. Sci. 24 (1) 73 - 86, February 2009. https://doi.org/10.1214/09-STS279

Information

Published: February 2009
First available in Project Euclid: 8 October 2009

zbMATH: 1327.65021
MathSciNet: MR2561131
Digital Object Identifier: 10.1214/09-STS279

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.24 • No. 1 • February 2009
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