On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood

In many applications, the parameters of interest are estimated by solving non‐smooth estimating functions with U‐statistic structure. Because the asymptotic covariances matrix of the estimator generally involves the underlying density function, resampling methods are often used to bypass the difficulty of non‐parametric density estimation. Despite its simplicity, the resultant‐covariance matrix estimator depends on the nature of resampling, and the method can be time‐consuming when the number of replications is large. Furthermore, the inferences are based on the normal approximation that may not be accurate for practical sample sizes. In this paper, we propose a jackknife empirical likelihood‐based inferential procedure for non‐smooth estimating functions. Standard chi‐square distributions are used to calculate the p‐value and to construct confidence intervals. Extensive simulation studies and two real examples are provided to illustrate its practical utilities.