Constructing Confidence Intervals for L-statistics Using Jackknife Empirical Likelihood

Abstract

The linear function of order statistics which is quite known as L-statistics has been widely used in non-parametric statistic such as location estimation and construction of tolerance level. The L-statistics include a family of statistics. The trimmed mean, Gini’s mean difference, and discard-deviation are all important L-statistics which have been well-investigated in relevant research. In order to make inference on L-statistics, we apply jackknife method to L-statistics and generate jackknife pseudo samples. There are two significant advantages of jackknifing the data. First, observations from the jackknife samples behave as if they were independent and identically distributed (iid) random variables. Second, the central limit theorem holds for jackknife samples under mild conditions, see, e.g Cheng [1], so the normal approximation method can be applied to the new sample to estimate the true values of L-statistics. In addition to normal approximation, we also apply jackknife empirical likelihood method to construct the confidence intervals for L-statistics. Our simulation and real-data application results both indicate that the jackknife empirical likelihood-based confidence intervals performs better than the normal approximation-based confidence intervals in terms of coverage probability and the length of confidence intervals.