On Empirical Likelihood Ratio Test for Equality of Means

by Aruna K. Rao and Aparna U.

Abstract: In this paper, empirical likelihood ratio test is proposed for equality of means of two distributions. Simulation is carried out to check the adequacy of the chi-square approximation with one degree of freedom and F approximation with (1, ) degrees of freedom where m and n denote the sample sizes, to the null distribution of the test statistic. The proposed test is compared to the t-test and the Wilcoxon-Mann-Whitney test when the variances of the two populations are unknown but equal. The simulation results indicate that the empirical likelihood ratio test has marginally smaller power compared to the t-test when the underlying distribution is normal. The empirical likelihood ratio test emerges as the best when the distributions are logistic, uniform, log-normal and gamma.

Key Words: Empirical likelihood ratio test, t-test, Wilcoxon-Mann-Whitney test, type I error rate, power comparison

Authors:
Aruna K. Rao, , arunaraomu@gmail.com
Aparna U

Editor: Abd-Elfattah A. M., a_afattah@hotmail.com On Empirical Likelihood Ratio Test for Equality of Means by Aruna K. Rao and Aparna U.

On Empirical Likelihood Ratio Test for Equality of Means

by Aruna K. Rao and Aparna U.

Abstract: In this paper, empirical likelihood ratio test is proposed for equality of means of two distributions. Simulation is carried out to check the adequacy of the chi-square approximation with one degree of freedom and F approximation with (1, ) degrees of freedom where m and n denote the sample sizes, to the null distribution of the test statistic. The proposed test is compared to the t-test and the Wilcoxon-Mann-Whitney test when the variances of the two populations are unknown but equal. The simulation results indicate that the empirical likelihood ratio test has marginally smaller power compared to the t-test when the underlying distribution is normal. The empirical likelihood ratio test emerges as the best when the distributions are logistic, uniform, log-normal and gamma.

Key Words: Empirical likelihood ratio test, t-test, Wilcoxon-Mann-Whitney test, type I error rate, power comparison

Authors:
Aruna K. Rao, , arunaraomu@gmail.com
Aparna U

Editor: Abd-Elfattah A. M., a_afattah@hotmail.com

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