On Bounded Completeness and The L1-Densensess of Likelihood Ratios

Marc Hallin, Bas Werker and Bo Zhou

No 2023-07, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

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 Farrell (1962) on a characterization of bounded completeness based on an L1 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 finitedimensional observation spaces are.

Keywords: sufficiency; completeness; ancillarity; Brownian motion; Mazur’s theorem (search for similar items in EconPapers)
Pages: 6 p.
Date: 2023-04
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