Some thoughts on Le Cam's statistical decision theory

Abstract

The paper contains some musings about the abstractions introduced by Lucien Le Cam into the asymptotic theory of statistical inference and decision theory. A short, self-contained proof of a key result (existence of randomizations via convergence in distribution of likelihood ratios), and an outline of a proof of a local asymptotic minimax theorem, are presented as an illustration of how Le Cam's approach leads to conceptual simplifications of asymptotic theory.