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Empirical Likelihood Ratio Tests for Homogeneity of Multiple Populations in the Presence of Auxiliary Information

Author

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  • Ronghuo Wu

    (Department of Mathemstics and Statistics, Yulin Normal University, Yulin 537000, China
    Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin 537000, China)

  • Yongsong Qin

    (Department of Statistics, Guangxi Normal University, Guilin 541004, China)

Abstract

The empirical likelihood ratio test (ELRT) statistic is constructed for testing the homogeneity of several nonparametric populations in the presence of some auxiliary information. It is shown—under some regularity conditions and under the null hypothesis that all distribution functions of the populations are equal—that the asymptotic distribution of the ELRT is a chi-squared distribution. The proposed ELRT could be more powerful than the Kruskal–Wallis test, as extra information can be efficiently employed by ELRT. The advantage of ELRT over T&P (2006) is that researchers do not need to select approximately normal statistics for inter-group comparisons, and ELRT is more suitable for the multi-population consistency test with a small sample size.

Suggested Citation

  • Ronghuo Wu & Yongsong Qin, 2022. "Empirical Likelihood Ratio Tests for Homogeneity of Multiple Populations in the Presence of Auxiliary Information," Mathematics, MDPI, vol. 10(13), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2341-:d:855648
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    References listed on IDEAS

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    2. Zhou, Yong & Wan, Alan T. K & Wang, Xiaojing, 2008. "Estimating Equations Inference With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1187-1199.
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