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.
Keywords
Cite
@article{arxiv.1107.3811,
title = {Some thoughts on Le Cam's statistical decision theory},
author = {David Pollard},
journal= {arXiv preprint arXiv:1107.3811},
year = {2011}
}
Comments
Unpublished paper written in 2000, shortly after Le Cam's death. "In correspondence during the summer of 1990, I discussed some of the ideas appearing in this paper with Lucien Le Cam. Even when he disagreed with my suggestions, or when I was "discovering" results that were already in his 1986 book or earlier work, he was invariably gracious, encouraging and helpful."