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Two-Stage Likelihood Ratio and Union-Intersection Tests for One-Sided Alternatives Multivariate Mean with Nuisance Dispersion Matrix

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  • Sen, Pranab K.
  • Tsai, Ming-Tien

Abstract

For a multinormal distribution with an unknown dispersion matrix, union-intersection (UI) tests for the mean against one-sided alternatives are considered. The null distribution of the UI test statistic is derived and its power monotonicity properties are studied. A Stain-type two-stage procedure is proposed to eliminate some of the inherent drawbacks of such tests. Some comparisons are also made with some recently proposed alternative conditional likelihood ratio tests.

Suggested Citation

  • Sen, Pranab K. & Tsai, Ming-Tien, 1999. "Two-Stage Likelihood Ratio and Union-Intersection Tests for One-Sided Alternatives Multivariate Mean with Nuisance Dispersion Matrix," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 264-282, February.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:2:p:264-282
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    References listed on IDEAS

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    1. N. Mukhopadhyay, 1980. "A consistent and asymptotically efficient two-stage procedure to construct fixed width confidence intervals for the mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 27(1), pages 281-284, December.
    2. Tsai, M. T. M., 1993. "UI Score Tests for Some Restricted Alternatives in Exponential Families," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 305-323, May.
    3. Tsai, Mingtan, 1992. "On the power superiority of likelihood ratio tests for restricted alternatives," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 102-109, July.
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    Cited by:

    1. Zhao, Junguang & Xu, Xingzhong, 2016. "A generalized likelihood ratio test for normal mean when p is greater than n," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 91-104.
    2. Rosa Arboretti & Fortunato Pesarin & Luigi Salmaso, 2021. "A unified approach to permutation testing for equivalence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1033-1052, September.

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