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November, 1981 A Complete Class Theorem for Statistical Problems with Finite Sample Spaces
Lawrence D. Brown
Ann. Statist. 9(6): 1289-1300 (November, 1981). DOI: 10.1214/aos/1176345645


This paper contains a complete class theorem (Theorem 3.2) which applies to most statistical estimation problems having a finite sample space. This theorem also applies to many other statistical problems with finite sample spaces. The description of this complete class involves a stepwise algorithm. At each step of the process it is necessary to construct the Bayes procedures in a suitably modified version of the original problem. The complete class is a minimal complete class if the loss function is strictly convex. Some examples are given to illustrate the application of this complete class theorem. Among these is a new result concerning the estimation of the parameters of a multinomial distribution under a normalized quadratic loss function. (See Example 4.5).


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Lawrence D. Brown. "A Complete Class Theorem for Statistical Problems with Finite Sample Spaces." Ann. Statist. 9 (6) 1289 - 1300, November, 1981.


Published: November, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0476.62006
MathSciNet: MR630111
Digital Object Identifier: 10.1214/aos/1176345645

Primary: 62C07
Secondary: 62C10 , 62C15 , 62F10 , 62F11

Keywords: Admissible procedures , Bayes procedure , Binomial distribution , Complete class theorem , estimation , finite sample space , maximum likelihood estimate , multinomial distribution , squared error loss , strictly convex loss

Rights: Copyright © 1981 Institute of Mathematical Statistics


Vol.9 • No. 6 • November, 1981
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