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A unified approach to testing for and against a set of linear inequality constraints in the product multinomial setting

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  • El Barmi, Hammou
  • Johnson, Matthew

Abstract

A problem that is frequently encountered in statistics concerns testing for equality of multiple probability vectors corresponding to independent multinomials against an alternative they are not equal. In applications where an assumption of some type of stochastic ordering is reasonable, it is desirable to test for equality against this more restrictive alternative. Similar problems have been considered heretofore using the likelihood ratio approach. This paper aims to generalize the existing results and provide a unified technique for testing for and against a set of linear inequality constraints placed upon on any probability vectors corresponding to r independent multinomials. The paper shows how to compute the maximum likelihood estimates under all hypotheses of interest and obtains the limiting distributions of the likelihood ratio test statistics. These limiting distributions are of chi bar square type and the expression of the weighting values is given. To illustrate our theoretical results, we use a real life data set to test against second-order stochastic ordering.

Suggested Citation

  • El Barmi, Hammou & Johnson, Matthew, 2006. "A unified approach to testing for and against a set of linear inequality constraints in the product multinomial setting," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1894-1912, September.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1894-1912
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    References listed on IDEAS

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    1. El Barmi, Hammou & Dykstra, Richard L., 1996. "Restricted product multinomial and product Poisson maximum likelihood estimation based upon Fenchel duality," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 117-123, August.
    2. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
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    Cited by:

    1. Hammou El Barmi, 2020. "A test for the presence of stochastic ordering under censoring: the k-sample case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 451-470, April.
    2. Chen-Yu Hong & Yu-Wei Chang & Rung-Ching Tsai, 2016. "Estimation of Generalized DINA Model with Order Restrictions," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 460-484, October.

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