完美和非完美中位数排序集抽样下刻度参数的极大似然估计  

Maximum Likelihood Estimator of Scale Parameter Under Perfect and Imperfect Median Ranked Set Sampling Design

作　　者：陈望学[1] 杨瑞 谢民育[2] CHEN WANGXUE;YANG RUI;XIE MINYU(Department of Mathematics and Statistics,Jishou Universtty,Jishou 416000,China;College of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China)

机构地区：[1]吉首大学数学与统计学院,吉首416000 [2]华中师范大学数学与统计学学院,武汉430079

出　　处：《应用数学学报》2020年第3期572-583,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学青年基金(11901236);湖南省自然科学青年基金(2019JJ50479);湖南省教育厅优秀青年基金(18B322);湖南省青年骨干教师项目(湘教通(2020)43号);湘西自治州基础理论研究基金(2018SF5026)资助项目.

摘　　要：当研究目标的实际测量具有不可修复的破坏性或耗资巨大时,有效的抽样设计将是一个重要的研究课题.在统计推断方面,排序集抽样(RSS)现在是被视为一种比简单随机抽样(SRS)更为有效的收集数据的方式.本文在中位数RSS(MRSS)下,研究了刻度参数的极大似然估计(MLE)及其性质.证明了该MLE在刻度变换群下是一个同变估计.以威布尔分布和正态分布为例,比较了MRSS,RSS和SRS下刻度参数的MLE的效率.数值结果表明不管排序是否完美,MRSS下刻度参数的MLE都是比RSS和(或)SRS下刻度参数的MLE有效.Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)is now regarded as an effective way in statistical inference and important alternative to simple random sampling(SRS).In the current paper,an extended of RSS called median RSS(MRSS)is considered for the estimation of the scale parameter.A maximum likelihood estimator(MLE)is studied and its properties are obtained under MRSS.We prove the MLE is an equivariant estimator under scale transformation.Their efficiencies with respect to the corresponding estimators based on RSS,MRSS and SRS are compared for the cases of weibull distribution and normal distribution.The method is studied under both perfect and imperfect ranking.It appears that the MLE of scale parameter using MRSS is a good competitor to that using RSS and(or)SRS.

关 键 词：排序集抽样 中位数排序集抽样 极大似然估计 

分 类 号：O212.2[理学—概率论与数理统计]