Open Access
Translator Disclaimer
January, 1978 Rank Order Estimation with the Dirichlet Prior
Gregory Campbell, Myles Hollander
Ann. Statist. 6(1): 142-153 (January, 1978). DOI: 10.1214/aos/1176344073

Abstract

Suppose that a sample of size $n$ from a distribution function $F$ is obtained. However, only $r(< n)$ values from the sample are observed, say $X_1,\cdots, X_r$. Without loss of generality, we can consider $X_1,\cdots, X_r$ to be the first $r$ values in the (unordered) sample. The problem is to estimate the rank order $G$ of $X_1$ among $X_1,\cdots, X_n$. The situations of interest include $F$ nonrandom, either known or unknown, and $F$ random. The random case assumes that $F$ is a random distribution function chosen according to Ferguson's (Ann. Statist. 1 (1973) 209-230) Dirichlet process prior. Since this random distribution function is discrete with probability one, average ranks are used to resolve ties. A Bayes estimator (squared-error loss) of $G$ is developed for the random model. For the nonrandom distribution function model, optimal non-Bayesian estimators are developed in both the case where $F$ is known and the case where $F$ is unknown. These estimators are compared with the Dirichlet estimator on the basis of average mean square errors under both the random and nonrandom models.

Citation

Download Citation

Gregory Campbell. Myles Hollander. "Rank Order Estimation with the Dirichlet Prior." Ann. Statist. 6 (1) 142 - 153, January, 1978. https://doi.org/10.1214/aos/1176344073

Information

Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0371.62070
MathSciNet: MR455198
Digital Object Identifier: 10.1214/aos/1176344073

Subjects:
Primary: 62G05
Secondary: 60K99

Keywords: Bayes procedure , Dirichlet process , Rank order estimation

Rights: Copyright © 1978 Institute of Mathematical Statistics

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.6 • No. 1 • January, 1978
Back to Top