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November, 1974 Minimal Sufficient Statistics for Families of Product Measures
D. Landers
Ann. Statist. 2(6): 1335-1339 (November, 1974). DOI: 10.1214/aos/1176342887

Abstract

It is shown in this paper that the product family of countably many families of perfect probability measures defined on countably generated $\sigma$-fields admits a minimal sufficient statistic if and only if each component family admits a minimal sufficient statistic. Moreover, the minimal sufficient statistic of the product family is the "product" of the minimal sufficient statistics for the component families. Examples show that the assumptions on the component families cannot be omitted.

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D. Landers. "Minimal Sufficient Statistics for Families of Product Measures." Ann. Statist. 2 (6) 1335 - 1339, November, 1974. https://doi.org/10.1214/aos/1176342887

Information

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

zbMATH: 0295.62005
MathSciNet: MR378160
Digital Object Identifier: 10.1214/aos/1176342887

Subjects:
Primary: 62B05

Keywords: minimal sufficient statistic , product measures

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 6 • November, 1974
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