排序集抽样下分布函数的非参数核估计  

Nonparametric Kernel Estimation of Distribution Function Under Ranked Set Sampling

作　　者：张良勇 董晓芳 樊祥嘉 ZHANG Liangyong;DONG Xiaofang;FAN Xiangjia(College of Statistics&Mathematics,Hebei University of Economics and Business,Shijiazhuang 050061)

机构地区：[1]河北经贸大学统计与数学学院,石家庄050061

出　　处：《系统科学与数学》2024年第8期2536-2548,共13页Journal of Systems Science and Mathematical Sciences

基　　金：河北省教育厅科学研究项目(ZD2022062)资助课题;。

摘　　要：排序集抽样方法适用于样本测量困难但排序容易的场合,已被广泛应用于临床医学、生态环境、农林业等领域.分布函数是概率统计中一个重要函数,为了提高未知总体分布函数的估计效率,文章基于排序集抽样方法,采用核估计思想和平均秩方法,构建了分布函数的非参数估计量,证明了其具有渐近无偏性、相合性和一致强相合性.估计效率通过估计量的积分均方误差来进行评价,渐近相对效率和模拟相对效率的研究结果表明:新建估计量的估计效率高于简单随机抽样下相应估计量,并且随着样本量的减小,新建估计量的相对优势越明显.最后,针叶树数据的应用结果进一步验证了理论研究结果的正确性.The ranked set sampling method is suitable for the situation where the sample measurement is difficult but the ranking is easy,and has been widely applied in clinical medicine,ecological environment,agriculture and forestry,and other fields.The distribution function is an important function in probability statistics.In order to improve the estimation efficiency of the distribution function of an unknown population,this paper adopts the kernel estimation idea and the average rank method to construct a nonparametric estimator of the distribution function based on the ranked set sampling method.The new estimator is shown to have asymptotic unbiasedness,consistency,and uniformly strong consistency.The estimation efficiency is evaluated by the mean integrated square error of the estimator.The research results of asymptotic relative efficiency and simulated relative efficiency show that the estimation efficiency of the new estimator is higher than that of the corresponding estimator under simple random sampling,and as the sample size decreases,the relative advantage of the new estimator becomes more apparent.Finally,the application results of coniferous tree data further verify the correctness of the theoretical research results.

关 键 词：排序集抽样 分布函数 非参数核估计 积分均方误差 

分 类 号：O212.1[理学—概率论与数理统计]