Order Restricted Statistical Tests on Multinomial and Poisson Parameters: The Starshaped Restriction

Open Access

1 December 1982

journal article
Published by Institute of Mathematical Statistics in The Annals of Statistics

Vol. 10 (4) , 1246-1252
https://doi.org/10.1214/aos/1176345989

Abstract

Likelihood ratio statistics for (i) testing the homogeneity of a collection of multinomial parameters against the alternative which accounts for the restriction that those parameters are starshaped (cf. Shaked, Ann. Statist., 1979), and for (ii) testing the null hypothesis that this parameter vector is starshaped, are considered. For both tests the asymptotic distribution of the test statistic under the null hypothesis is a version of the Chi-bar-square distribution. Analogous tests on a collection of Poisson means are also found to have asymptotic Chi-bar-square distributions.

Keywords

ASYMPTOTIC DISTRIBUTION
VECTOR ANALYSIS
POISSON EQUATION
THEOREMS
ASYMPTOTIC SERIES
POISSON
STATISTICAL TEST
CHI SQUARE TEST
LIKELIHOOD RATIO TEST
STATISTICAL TESTS
PARAMETERS
MULTIVARIATE ANALYSIS
MAXIMUM LIKELIHOOD
MULTINOMIAL

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