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A two sample nonparametric test for variability via empirical likelihood methods

Author

Listed:
  • Lisa Parveen

    (Indian Institute of Engineering Science and Technology, Shibpur)

  • Ruhul Ali Khan

    (University of Arizona)

  • Murari Mitra

    (Indian Institute of Engineering Science and Technology, Shibpur)

Abstract

Comparison of variability or dispersion of two distributions is the major focus of this work. To this end, we consider a two sample testing problem for detecting dominance in dispersive order and develop a test based on U-statistic approach. We also explore a link between the two measures of variability, viz. dispersive order and Gini’s mean difference (GMD). We exploit methodologies based on jackknife empirical likelihood (JEL) and adjusted JEL in order to overcome certain practical difficulties. The performance of the proposed test is assessed by means of a simulation study. Finally, we apply our test in the context of several real life situations including medical studies and insurance data.

Suggested Citation

  • Lisa Parveen & Ruhul Ali Khan & Murari Mitra, 2024. "A two sample nonparametric test for variability via empirical likelihood methods," Statistical Papers, Springer, vol. 65(7), pages 4243-4265, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01555-z
    DOI: 10.1007/s00362-024-01555-z
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    References listed on IDEAS

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    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. Bartoszewicz, Jaroslaw, 1986. "Dispersive ordering and the total time on test transformation," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 285-288, October.
    3. Denneberg, Dieter, 1990. "Premium Calculation: Why Standard Deviation Should be Replaced by Absolute Deviation1," ASTIN Bulletin, Cambridge University Press, vol. 20(2), pages 181-190, November.
    4. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    5. Bartoszewicz, Jaroslaw, 1992. "Asymptotic distributions of tests for dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 15(1), pages 11-20, September.
    6. Belzunce, F. & Candel, J. & Ruiz, J. M., 1996. "Dispersive orderings and characterization of ageing classes," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 321-327, August.
    7. Jiayin Zheng & Junshan Shen & Shuyuan He, 2014. "Adjusted empirical likelihood for right censored lifetime data," Statistical Papers, Springer, vol. 55(3), pages 827-839, August.
    8. Pellerey, Franco & Shaked, Moshe, 1997. "Characterizations of the IFR and DFR aging notions by means of the dispersive order," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 389-393, May.
    9. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2021. "Tests for Laplace order dominance with applications to insurance data," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 163-173.
    10. Y Cheng & Y Zhao, 2019. "Bayesian jackknife empirical likelihood," Biometrika, Biometrika Trust, vol. 106(4), pages 981-988.
    11. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    12. Mathew, Litty & P., Anisha & Kattumannil, Sudheesh K., 2022. "A jackknife empirical likelihood ratio test for strong mean inactivity time order," Statistics & Probability Letters, Elsevier, vol. 190(C).
    13. Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
    14. Zhao, Peng & Balakrishnan, N., 2011. "New results on comparisons of parallel systems with heterogeneous gamma components," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 36-44, January.
    15. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    16. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    17. Chakravarty, Satya R, 1988. "Extended Gini Indices of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 147-156, February.
    18. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.
    19. Fan, Yanqin, 1999. "A data-driven test for dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 331-336, February.
    20. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
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