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 , 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.
A 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.
Constructing Confidence Intervals for L-statistics Using Jackknife Empirical Likelihood.
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