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Jackknife empirical likelihood inference for the mean absolute deviation

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  • Zhao, Yichuan
  • Meng, Xueping
  • Yang, Hanfang

Abstract

In statistics mean absolute deviation plays an important role in measuring spread of a data. In this paper, we focus on using the jackknife, the adjusted and the extended jackknife empirical likelihood methods to construct confidence intervals for the mean absolute deviation of a random variable. The empirical log-likelihood ratio statistic is derived whose asymptotic distribution is a standard chi-square distribution. The results of simulation study show the comparison of the average length and coverage probability by using jackknife empirical likelihood methods and normal approximation method. The proposed adjusted and extended jackknife empirical likelihood methods perform better than other methods, in particular for skewed distributions. We use real data sets to illustrate the proposed jackknife empirical likelihood methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:91:y:2015:i:c:p:92-101
    DOI: 10.1016/j.csda.2015.06.001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Amorim, G. & Thas, O. & Vermeulen, K. & Vansteelandt, S. & De Neve, J., 2018. "Small sample inference for probabilistic index models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 137-148.
    2. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    3. Yu, Xue & Zhao, Yichuan, 2019. "Empirical likelihood inference for semi-parametric transformation models with length-biased sampling," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 115-125.
    4. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    5. 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.
    6. Hui-Ling Lin & Zhouping Li & Dongliang Wang & Yichuan Zhao, 2017. "Jackknife empirical likelihood for the error variance in linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 151-166, April.
    7. Xue Yu & Yichuan Zhao, 2019. "Jackknife empirical likelihood inference for the accelerated failure time model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 269-288, March.
    8. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.

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