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Extended MaxT Tests of One-Sided Hypotheses

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  • Zeng-Hua Lu

Abstract

In many statistical applications of one-sided tests of multiple hypotheses researchers are often concerned not only with global tests of the intersection of individual hypotheses, but also with multiple tests of individual hypotheses. For example, in clinical trial studies researchers often need to find out the efficacy of a treatment, as well as the significance of each outcome measurement (endpoint) of the treatment. This article proposes MaxT type tests aiming at improving the global power of existing MaxT tests. Our extended MaxT tests are constructed by adding an extra component to the maximand set of existing MaxT tests. The added component is a weighted sum of other components. Some power properties relating to choices of weight are studied. Our simulation study shows that the proposed tests can considerably improve the global power of existing MaxT tests and can also outperform many other global tests under some alternatives and/or some nonnormal distributions. Furthermore, it is shown that such global power improvement may involve little loss of power on multiple testing. Two real data examples on clinical trial studies reported in the literature are reexamined. The results of our tests suggest stronger evidence on treatment effects over MaxT tests and likelihood ratio tests while changing little on the evidence concerning endpoint testing. Supplementary materials for this article are available online.

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  • 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.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:423-437
    DOI: 10.1080/01621459.2015.1019509
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    References listed on IDEAS

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    1. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    2. Richard M. Bittman & Joseph P. Romano & Carlos Vallarino & Michael Wolf, 2009. "Optimal testing of multiple hypotheses with common effect direction," Biometrika, Biometrika Trust, vol. 96(2), pages 399-410.
    3. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    4. Romano Joseph P. & Shaikh Azeem & Wolf Michael, 2011. "Consonance and the Closure Method in Multiple Testing," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-25, February.
    5. Maxwell King & Ping Wu, 1997. "Locally optimal one-sided tests for multiparameter hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 131-156.
    6. Lu, Zeng-Hua, 2013. "Halfline tests for multivariate one-sided alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 479-490.
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    Cited by:

    1. Canepa Alessandra, 2022. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Journal of Time Series Econometrics, De Gruyter, vol. 14(1), pages 51-85, January.
    2. Zeng-Hua Lu, 2019. "Extended MinP Tests for Global and Multiple testing," Papers 1911.04696, arXiv.org, revised Aug 2024.
    3. Zeng-Hua Lu, 2020. "Bahadur intercept with applications to one-sided testing," Statistical Papers, Springer, vol. 61(2), pages 645-658, April.
    4. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    5. Giuseppe Cavaliere & Zeng-Hua Lu & Anders Rahbek & Yuhong Yang, 2021. "MinP Score Tests with an Inequality Constrained Parameter Space," Papers 2107.06089, arXiv.org.
    6. Zeng-Hua Lu & Alec Zuo, 2017. "Child disability, welfare payments, marital status and mothers’ labor supply: Evidence from Australia," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1339769-133, January.

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