On Bounded Completeness and the $L_1$-Denseness of Likelihood Ratios
Statistics Theory
2023-08-03 v1 Statistics Theory
Abstract
The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this short note, we provide a direct proof of a little-known result by \cite{Far62} on a characterization of bounded completeness based on an denseness property of the linear span of likelihood ratios. As an application, we show that an experiment with infinite-dimensional observation space is boundedly complete iff suitably chosen restricted subexperiments with finite-dimensional observation spaces are.
Keywords
Cite
@article{arxiv.2308.00895,
title = {On Bounded Completeness and the $L_1$-Denseness of Likelihood Ratios},
author = {Marc Hallin and Bas Werker and Bo Zhou},
journal= {arXiv preprint arXiv:2308.00895},
year = {2023}
}