Superefficiency from the Vantage Point of Computability

Abstract

In 1952 Lucien Le Cam announced his celebrated result that, for regular univariate statistical models, sets of points of super- efficiency have Lebesgue measure zero. After reviewing the turbulent history of early studies of superefficiency, I suggest using t he notion of computability as a tool for exploring the phenomenon of superef- ficiency. 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 areeven countable.