分位数置信区间的估计方法分析  

Analysis for Estimation Methods of Confidence Interval of Quantile

作　　者：牛司丽 NIU Si-li(School of Mathematical Sciences,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《数学的实践与认识》2020年第18期114-119,共6页Mathematics in Practice and Theory

基　　金：国家社科基金(17BTJ032)。

摘　　要：构造了基于分位数两种估计量的渐近置信区间,并找到分位数基于样本次序统计量的渐近置信区间.同时,建立了基于分布函数核估计定义的分位数估计量的渐近正态性,并使用经验似然方法构造出分位数的两种渐近置信区间.在模拟分析中,基于置信区间的平均长度和覆盖率,分析构造分位数的五种渐近置信区间的有限样本表现.In this paper,we construct two asymptotic confidence intervals of the quantile based on its two kinds of estimators,and find the asymptotic confidence interval of the quantile based on the order statistic.Meanwhile,the asymptotic normality of the estimator,which is defined by kernel estimator of distribution,for the quantile is established.Also,we employ the method of empirical likelihood to construct two asymptotic confidence intervals of the quantile.In simulation study,finite sample performance of five asymptotic confidence intervals of the quantile are analyzed based on the average length and coverage probability of the asymptotic confidence intervals.

关 键 词：渐近正态性 置信区间 经验似然 次序统计量 分位数 

分 类 号：O212.1[理学—概率论与数理统计]