The Annals of Statistics

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

Richard L. Dykstra and Tim Robertson

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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.

Article information

Source
Ann. Statist., Volume 10, Number 4 (1982), 1246-1252.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345989

Digital Object Identifier
doi:10.1214/aos/1176345989

Mathematical Reviews number (MathSciNet)
MR673659

Zentralblatt MATH identifier
0519.62023

JSTOR
links.jstor.org

Subjects
Primary: 62F05: Asymptotic properties of tests
Secondary: 62E15: Exact distribution theory

Keywords
Star shaped orderings multinomial Poisson likelihood ratio tests Chi-bar-square distributions maximum likelihood

Citation

Dykstra, Richard L.; Robertson, Tim. Order Restricted Statistical Tests on Multinomial and Poisson Parameters: The Starshaped Restriction. Ann. Statist. 10 (1982), no. 4, 1246--1252. doi:10.1214/aos/1176345989. https://projecteuclid.org/euclid.aos/1176345989


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Corrections

  • See Correction: Richard L. Dykstra, Tim Robertson. Correction: Order Restricted Statistical Tests on Multinomial and Poisson Parameters: The Starshaped Restriction. Ann. Statist., Volume 15, Number 1 (1987), 469--469.