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Extended MinP Tests of Multiple Hypotheses

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  • Zeng-Hua Lu

Abstract

Much empirical research in economics and finance involves simultaneously testing multiple hypotheses. This paper proposes extended MinP (EMinP) tests by expanding the minimand set of the MinP test statistic to include the $p$% -value of a global test such as a likelihood ratio test. We show that, compared with MinP tests, EMinP tests may considerably improve the global power in rejecting the intersection of all individual hypotheses. Compared with closed tests EMinP tests have the computational advantage by sharing the benefit of the stepdown procedure of MinP tests and can have a better global power over the tests used to construct closed tests. Furthermore, we argue that EMinP tests may be viewed as a tool to prevent data snooping when two competing tests that have distinct global powers are exploited. Finally, the proposed tests are applied to an empirical application on testing the effects of exercise.

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  • Zeng-Hua Lu, 2019. "Extended MinP Tests of Multiple Hypotheses," Papers 1911.04696, arXiv.org.
    • Handle: RePEc:arx:papers:1911.04696
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    References listed on IDEAS

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    1. John A. List & Azeem M. Shaikh & Yang Xu, 2019. "Multiple hypothesis testing in experimental economics," Experimental Economics, Springer;Economic Science Association, vol. 22(4), pages 773-793, December.
    2. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    3. Romano, Joseph P. & Shaikh, Azeem M. & Wolf, Michael, 2008. "Formalized Data Snooping Based On Generalized Error Rates," Econometric Theory, Cambridge University Press, vol. 24(2), pages 404-447, April.
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    5. Gary Charness & Uri Gneezy, 2009. "Incentives to Exercise," Econometrica, Econometric Society, vol. 77(3), pages 909-931, May.
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    7. 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.
    8. 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.
    9. 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.
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    13. 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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