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Halfline tests for multivariate one-sided alternatives

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  • Lu, Zeng-Hua

Abstract

Halfline tests studied in this paper are t type tests for testing inequality constraints under the alternative hypothesis. An appealing example of such tests in the literature is to find a halfline in the restricted parameter space such that the resultant test is most stringent in terms of the minimization of the maximum shortcoming. However, there appears to be no generally applicable procedure available for implementing this test. This paper is to fill this gap. We also propose a halfline test which has a computational advantage. Simulation studies are conducted to compare the finite sample performance of halfline tests against some existing tests. The results of our simulation studies suggest that halfline tests can have a better finite sample power property and are more robust against the normality assumption compared to likelihood ratio-based tests.

Suggested Citation

  • Lu, Zeng-Hua, 2013. "Halfline tests for multivariate one-sided alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 479-490.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:479-490
    DOI: 10.1016/j.csda.2012.07.016
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    References listed on IDEAS

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    1. Hillier, Grant, 1986. "Joint Tests for Zero Restrictions on Non-negative Regression Coefficients," MPRA Paper 15804, University Library of Munich, Germany.
    2. Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
    3. King, Maxwell L. & Smith, Murray D., 1986. "Joint one-sided tests of linear regression coefficients," Journal of Econometrics, Elsevier, vol. 32(3), pages 367-383, August.
    4. Larocque D. & Labarre M., 2004. "A Conditionally Distribution-Free Multivariate Sign Test for One-Sided Alternatives," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 499-509, January.
    5. Cohen, A. & Kemperman, J. H. B. & Sackrowitz, H. B., 1993. "Unbiased Tests for Normal Order Restricted Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 139-153, July.
    6. Sepanski, Steven J., 1996. "Asymptotics for multivariate t-statistic for random vectors in the generalized domain of attraction of the multivariate normal law," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 179-188, October.
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    Cited by:

    1. Zeng-Hua Lu, 2016. "Extended MaxT Tests of One-Sided Hypotheses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 423-437, March.
    2. Zeng-Hua Lu, 2019. "Extended MinP Tests for Global and Multiple testing," Papers 1911.04696, arXiv.org, revised Aug 2024.
    3. Giuseppe Cavaliere & Zeng-Hua Lu & Anders Rahbek & Yuhong Yang, 2021. "MinP Score Tests with an Inequality Constrained Parameter Space," Papers 2107.06089, arXiv.org.

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