基于样本次序统计量的总体分位数的非参数统计推断  

Non-parametric Statistical Inference for the Population Quantiles Based on Order Statistics of Samples

作　　者：赵旭[1] 程维虎[1] ZHAO Xu;CHENG WEIHU(Faculty of Science,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学理学部,北京100124

出　　处：《应用数学学报》2021年第4期475-491,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11801019);北京市自然科学基金重点研究专题(Z190021)资助项目。

摘　　要：随机总体分位数的统计推断理论与方法一直是统计学研究的重要课题.其主要原因是分位数的应用涉及众多领域,且在各领域的研究中起到举足轻重的作用.本文系统地论述了基于样本次序统计量的总体分位数的非参数统计推断的理论和方法;给出了基于样本次序统计量的总体分位数的估计方法,总体两个分位数之差的置信区间,总体容许区间的求解方法及符号检验.希望有助于读者的科研与应用.Statistical inference theory and methods of the population quantiles have always been an important topic in statistical research,mainly because the application of quantile involves many fields,and it plays a decisive role in the research of various fields.This review paper summarizes the current progresses of quantile estimation.We discuss the theory and methods of non-parametric statistical inference systematically based on the population quantile of sample order statistics.The interval estimation of the population quantile and the difference between the population quantile,the tolerance interval of the population,and sign test are given in this paper.These will help readers in scientific research and application.

关 键 词：非参数推断 次序统计量 总体分位数 置信区间 容许区间 

分 类 号：O212.7[理学—概率论与数理统计]