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On the test for the homogeneity of a parameter matrix with some rows constrained by synchronized order restrictions

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  • Hu, Xiaomi
  • Banerjee, Arijit

Abstract

The tests on the homogeneity of the columns of the coefficient matrix in a multiple multivariate linear regression with some rows of the matrix constrained by synchronized orderings, using the test statistics obtained by replacing the unknown variance–covariance matrix with its estimator in likelihood ratio test statistics, form a family of ad hoc tests. It is shown in this paper that the tests in the family share the same alpha-level critical values and follow the same distributions for computing their p-values. A sufficient condition is established for other tests to enjoy these properties, and to be more powerful. Two such more powerful tests are examined.

Suggested Citation

  • Hu, Xiaomi & Banerjee, Arijit, 2012. "On the test for the homogeneity of a parameter matrix with some rows constrained by synchronized order restrictions," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 64-70.
    • Handle: RePEc:eee:jmvana:v:107:y:2012:i:c:p:64-70
    DOI: 10.1016/j.jmva.2012.01.006
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    References listed on IDEAS

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    1. Hu, Xiaomi, 2009. "p-values of a test on homogeneous means in a multivariate isotonic regression," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2005-2011, October.
    2. Silvapulle, M. J., 1995. "A Hotelling's T2-Type Statistic for Testing against One-Sided Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 312-319, November.
    3. Hu, Xiaomi, 2007. "Multivariate Analysis Without "vec" and """," The American Statistician, American Statistical Association, vol. 61, pages 64-66, February.
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    Cited by:

    1. Hamdan, Mustafa & Hu, Xiaomi, 2019. "Unbiasedness of LRT on the homogeneity of means in MANOVA under general order restrictions," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 59-65.
    2. Asfha, Huruy & Hu, Xiaomi, 2023. "An algorithm for a pseudo RMLE under simple tree multivariate order restriction," Statistics & Probability Letters, Elsevier, vol. 202(C).

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