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A distribution-free test of independence based on a modified mean variance index

Statistical Theory and Related Fields 2023年第3期7卷 235-259页

作者： Weidong Ma Fei Ye Jingsong Xiao Ying Yang Department of Mathematical Sciences Tsinghua UniversityBeijingPeople’s Republic of China School of Statistics Capital University o fEconomics and BusinessBeijingPeople’s Republic of China

Cui and Zhong(2019),(Computational Statistics&Data Analysis,139,117–133)proposed a test based on the mean variance(MV)index to test independence between a categorical random variable Y with R categories and a continuous random variable *** ingeniously proved the asymptotic normality of the MV test statistic when R diverges to infinity,which brings many merits to the MV test,including making it more convenient for independence testing when R is *** paper considers a new test called the integral Pearson chi-square(IPC)test,whose test statistic can be viewed as a modified MV test statistic.A central limit theorem of the martin-gale difference is used to show that the asymptotic null distribution of the standardized IPC test statistic when R is diverging is also a normal distribution,rendering the IPC test sharing many merits with the MV *** an application of such a theoretical finding,the IPC test is extended to test independence between continuous random *** finite sample performance of the proposed test is assessed by Monte Carlo simulations,and a real data example is presented for illustration.

关键词： Test of independence asymptotic null distribution mean variance index k-sample Anderson Darling test statistic concentration type inequality

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Power analysis,sample size calculation for testing the largest binomial probability

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Statistical Theory and Related Fields 2020年第1期4卷 78-83页

作者： Thuan Nguyen Jiming Jiang Oregon Health and Science University PortlandORUSA University of California DavisCAUSA

A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of *** is shown that the asymptotic null distribution of the likelihood-ratio statistic is not parameterfree,but χ_(1)^(2) is a conservative asymptotic null distribution.A nonlinear Gauss-Seidel algorithm is proposed to uniquely determine the alternative for the power and sample size calculation given the baseline binomial *** example from an animal clinical trial is discussed.

关键词： asymptotic null distribution binomial probability complex hypotheses Gauss-Seidel logistic regression power sample size tests

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