Superefficiency from the Vantage Point of Computability

Details Superefficiency from the Vantage Point of Computability Superefficiency from the Vantage Point of Computability

2008-08-16

arxiv.org/abs/0808.2266v2

Statistical Science 2009, Vol. 24, No. 1, 73-86

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-STS279 the Statistical Science (http://www.imstat.org/sts/) by the Institute of M

Scientific paper

10.1214/09-STS279

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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