## The Annals of Statistics

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

### A Complete Class Theorem for Statistical Problems with Finite Sample Spaces

#### 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