Some thoughts on Le Cam's statistical decision theory

TL;DR

This paper discusses Le Cam's abstract approach to asymptotic statistical decision theory, providing simplified proofs and insights into the foundational concepts and minimax theorems.

Contribution

It offers a self-contained proof of a key result and outlines a proof of a local asymptotic minimax theorem, illustrating the conceptual advantages of Le Cam's framework.

Findings

Simplified proof of existence of randomizations via likelihood ratios convergence

Outline of a proof for the local asymptotic minimax theorem

Demonstrates conceptual simplifications in asymptotic 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.