The Annals of Statistics

A Complete Class Theorem for Statistical Problems with Finite Sample Spaces

Lawrence D. Brown

Full-text: Open access

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).

Article information

Source
Ann. Statist., Volume 9, Number 6 (1981), 1289-1300.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345645

Digital Object Identifier
doi:10.1214/aos/1176345645

Mathematical Reviews number (MathSciNet)
MR630111

Zentralblatt MATH identifier
0476.62006

JSTOR
links.jstor.org

Subjects
Primary: 62C07: Complete class results
Secondary: 62C15: Admissibility 62F10: Point estimation 62F11 62C10: Bayesian problems; characterization of Bayes procedures

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

Citation

Brown, Lawrence D. A Complete Class Theorem for Statistical Problems with Finite Sample Spaces. Ann. Statist. 9 (1981), no. 6, 1289--1300. doi:10.1214/aos/1176345645. https://projecteuclid.org/euclid.aos/1176345645


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