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September, 1974 On the Existence of a Minimal Sufficient Subfield
Minoru Hasegawa, Michael D. Perlman
Ann. Statist. 2(5): 1049-1055 (September, 1974). DOI: 10.1214/aos/1176342826


Let $(X, S)$ be a measurable space and $M$ a collection of probability measures on S. Pitcher (Pacific J. Math. (1965), pages 597-611) introduced a condition called compactness on the statistical structure $(X, S, M)$, more general than domination by a fixed $\sigma$-finite measure. Under this condition he gave a construction of a minimal sufficient subfield. In this paper a counterexample invalidating this construction is presented. We give a nonconstructive proof of the existence of a minimal sufficient subfield under a condition slightly weaker than compactness. The proof proceeds by considering the intersection of an uncountable collection of sufficient subfields, and relies on a martingale convergence theorem with directed index set, due to Krickeberg.


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Minoru Hasegawa. Michael D. Perlman. "On the Existence of a Minimal Sufficient Subfield." Ann. Statist. 2 (5) 1049 - 1055, September, 1974.


Published: September, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0291.62006
MathSciNet: MR375544
Digital Object Identifier: 10.1214/aos/1176342826

Primary: 62B05

Keywords: Coherence , compactness , discrete family , dominated family , intersection of sufficient subfields , martingale , Minimal sufficient subfield

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 5 • September, 1974
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