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July, 1975 Characterizations of Prediction Sufficiency (Adequacy) in Terms of Risk Functions
Kei Takeuchi, Masafumi Akahira
Ann. Statist. 3(4): 1018-1024 (July, 1975). DOI: 10.1214/aos/1176343206


Prediction sufficiency (adequacy), as it is usually defined in terms of conditional expectations, does imply "real" prediction sufficiency; i.e. sufficiency in terms of risk functions. The converse holds provided we permit the loss to depend on the unknown parameter. This is no longer true if we insist on loss functions which do not involve the unknown parameter. Conditional independence still holds but ordinary sufficiency may fail. If, however, we require equivalence of risk functions, then ordinary sufficiency and, consequently, prediction sufficiency follows.


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Kei Takeuchi. Masafumi Akahira. "Characterizations of Prediction Sufficiency (Adequacy) in Terms of Risk Functions." Ann. Statist. 3 (4) 1018 - 1024, July, 1975.


Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0333.62010
MathSciNet: MR375546
Digital Object Identifier: 10.1214/aos/1176343206

Primary: 62B05
Secondary: 62C07

Keywords: Conditional independence , equality of risk functions , Prediction sufficiency

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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