Partially Complete Sufficient Statistics Are Jointly Complete

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https://epubs.siam.org/doi/abs/10.1137/S0040585X97T987223

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https://doi.org/10.1137/S0040585X97T987223
 http://hdl.handle.net/11603/36932

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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Author/Creator ORCID

https://orcid.org/0000-0003-2888-674X

Date

2015

Type of Work

journal articles
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Citation of Original Publication

Kagan, A. M., Y. Malinovsky, and L. Mattner. “Partially Complete Sufficient Statistics Are Jointly Complete.” Theory of Probability & Its Applications 59, no. 3 (January 2015): 359–74. https://doi.org/10.1137/S0040585X97T987223.

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© 2015, Society for Industrial and Applied Mathematics.

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Abstract

The theorem formulated in the title (surprisingly, the result has been overlooked for many years) complements the theory of sufficient statistics in the part related to Lehmann--Scheffé completeness. Two proofs of the main result are given: The first, analytical, follows Landers and Rogge [Scand. J. Statist., 3 (1976), p. 139], while the second, purely statistical, uses the theory of optimal unbiased estimation in a relatively little known version completed by Schmetterer and Strasser [Anz. Österreich. Akad. Wiss. Math.-Naturwiss. Kl., 1974, no. 6, pp. 59--66]. Connections to previous results are discussed and illustrative examples are presented.