Statistics Papers

Document Type

Journal Article

Date of this Version

1981

Publication Source

Annals of Statistics

Volume

9

Issue

6

Start Page

1289

Last Page

1300

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).

Keywords

complete class theorem, finite sample space, admissible procedures, Bayes procedure, estimation, binomial distribution, multinomial distribution, strictly convex loss, squared error loss, maximum likelihood estimate

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Date Posted: 27 November 2017

This document has been peer reviewed.