Wang, Fuli2020-06-162020-06-162020-06-16https://hdl.handle.net/11299/213974A Project submitted to the faculty of the Graduate School of the University of Minnesota Duluth by Fuli Wang in partial fulfillment of the requirements for the degree of Master of Science, June 16, 2020. Advisor: Dr. Yongcheng Qi.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.enL-statisticsJackknifeEmpirical likelihood methodNormal approximationConfidence intervalsDepartment of Mathematics and StatisticsMaster of ScienceSwenson College of Science and EngineeringUniversity of Minnesota DuluthPlan Bs (project-based master's degrees)Master of Science in Mathematical SciencesScholarly Text or Essay