Title

Testing for the Supremacy of a Multinomial Cell Probability

Campus Units

Statistics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

9-2009

Journal or Book Title

Journal of the American Statistical Association

Volume

104

Issue

487

First Page

1052

Last Page

1059

DOI

10.1198/jasa.2009.tm08213

Abstract

Tests for the supremacy of a multinomial cell probability are developed. The tested null hypothesis states that a particular cell of interest is not more probable than all others. Rejection of this null leads to the conclusion that the cell of interest has a strictly greater probability than all other cells. The null hypothesis constrains the multinomial probability vector to a nonconvex region that is a union of closed convex cones. The likelihood ratio test for this problem is derived and shown to be equivalent to an intersection–union test. The least favorable configuration of the multinomial probability vector in the null parameter space is derived, and the limiting null distribution of the test statistic that is stochastically greatest is shown to be a mixture of point mass at zero and a chi-square distribution with a single degree of freedom. Asymptotic and valid finite-sample testing procedures are proposed and examined via a simulation study and the analysis of two datasets. The proposed procedures are extended to test whether the cell with the largest observed frequency is uniquely most probable. An equivalence between a likelihood ratio test for this problem and a union–intersection test is demonstrated.

Comments

This is a manuscript of an article published as Nettleton, Dan. "Testing for the supremacy of a multinomial cell probability." Journal of the American Statistical Association104, no. 487 (2009): 1052-1059. doi: 10.1198/jasa.2009.tm08213. Posted with permission.

Copyright Owner

American Statistical Association

Language

en

File Format

application/pdf

Published Version

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