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June, 1949 Sufficiency, Truncation and Selection
John W. Tukey
Ann. Math. Statist. 20(2): 309-311 (June, 1949). DOI: 10.1214/aoms/1177730042


The fact that the mean and variance were sufficient statistics for a univariate normal distribution truncated at a fixed point was known to Fisher by 1931 [2]. Hotelling [3] has recently observed the corresponding fact for the truncated multivariate normal distribution. It is the aim of this note to point out that these are special cases of a general result, namely: If a family of distributions admits a set of sufficient statistics, then the family obtained by truncation to a fixed set, or by fixed selection, also admits the SAME set of sufficient statistics.


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John W. Tukey. "Sufficiency, Truncation and Selection." Ann. Math. Statist. 20 (2) 309 - 311, June, 1949.


Published: June, 1949
First available in Project Euclid: 28 April 2007

zbMATH: 0041.26202
MathSciNet: MR30171
Digital Object Identifier: 10.1214/aoms/1177730042

Rights: Copyright © 1949 Institute of Mathematical Statistics

Vol.20 • No. 2 • June, 1949
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