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.

中文翻译：

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非光滑U结构方程的基于深度的加权折刀经验似然

在许多应用中，通过使用U解一些非光滑估计方程来估计感兴趣的参数统计结构。折刀经验似然法（JEL）可以通过降低经验似然法（EL）的计算复杂度来有效解决此问题。但是，作为EL，JEL遭受离群值的敏感性问题。在本文中，我们提出了加权折刀经验似然（WJEL）来解决JEL的上述局限性。拟议的WJEL通过为异常值分配较小的权重来倾斜JEL函数。导出WJEL比率统计量的渐近线。它的分布收敛为卡方随机变量的倍数。乘法常数取决于加权方案。WJEL比率的自归一化版本不需要知道常数，因此可以在极限范围内产生标准卡方分布。