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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

Abstract

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).

Citation

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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. https://doi.org/10.1214/aos/1176345645

Information

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

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

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

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 6 • November, 1981
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