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Depth-based weighted jackknife empirical likelihood for non-smooth U-structure equations

Author

Listed:
  • Yongli Sang

    (University of Louisiana at Lafayette)

  • Xin Dang

    (University of Mississippi)

  • Yichuan Zhao

    (Georgia State University)

Abstract

In many applications, parameters of interest are estimated by solving some non-smooth estimating equations with U-statistic structure. Jackknife empirical likelihood (JEL) approach can solve this problem efficiently by reducing the computation complexity of the empirical likelihood (EL) method. However, as EL, JEL suffers the sensitivity problem to outliers. In this paper, we propose a weighted jackknife empirical likelihood (WJEL) to tackle the above limitation of JEL. The proposed WJEL tilts the JEL function by assigning smaller weights to outliers. The asymptotic of the WJEL ratio statistic is derived. It converges in distribution to a multiple of a chi-square random variable. The multiplying constant depends on the weighting scheme. The self-normalized version of WJEL ratio does not require to know the constant and hence yields the standard chi-square distribution in the limit. Robustness of the proposed method is illustrated by simulation studies and one real data application.

Suggested Citation

  • Yongli Sang & Xin Dang & Yichuan Zhao, 2020. "Depth-based weighted jackknife empirical likelihood for non-smooth U-structure equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 573-598, June.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:2:d:10.1007_s11749-019-00667-1
    DOI: 10.1007/s11749-019-00667-1
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    References listed on IDEAS

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