An all-or-nothing phenomenon for superefficiency
Vladimir Vovk · arXiv (Cornell University) · 2008
In his 1953 paper Lucien Le Cam proved for regular univariate statistical models that sets of points of superefficiency have Lebesgue measure zero (in fact, these sets are even countable). Considering only computable estimators, it is possible to show that no computable parameter point can be a point of superefficiency. This strengthens Le Cam’s result to a dichotomy: either a parameter point θ can be computably estimated with zero error, or no computable estimator is more efficient at θ than the maximum likelihood estimator. 1