排序集抽样下Power-law分布中参数的参数估计  

Parametric Estimator of the Parameter of the Power-Law Distribution Under Ranked Set Sampling

作　　者：杨瑞 陈望学[1] 沈炳良 龙春先 YANG Rui;CHEN Wangxue;SHEN Bingliang;LONG Chunxian(Department of Mathematics and Statistics,Jishou University,Jishou 416000)

机构地区：[1]吉首大学数学与统计学院,吉首416000

出　　处：《系统科学与数学》2020年第2期308-317,共10页Journal of Systems Science and Mathematical Sciences

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);湖南省自教育厅优秀青年基金(18B322);湘西自治州基础理论研究基金(2018SF5026);湖南省第四次全国经济普查中标课题(湘经普办[2020]1号)资助课题。

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项重要的研究课题.在统计推断方面,排序集抽样(RSS)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.文章分别在SRS和RSS下研究了Power-law分布中参数的极大似然估计(MLE),修正MLE,修正无偏估计和修正最优线性无偏估计(BLUE).进一步针对该分布,文章找到了基于次序统计量Fisher信息量最大化的RSS,并在这种RSS下研究了上述估计.模拟结果显示RSS下的对应估计一致优于SRS下的对应估计.Cost effective sampling will be an important research problem in some experiments especially when the measurement of the characteristic of interest is costly or painful.Ranked set sampling(RSS)is now regarded as an effective tool in statistical inference and important alternative to simple random sampling(SRS).In this article,several traditional estimators of the parameter such as maximum likelihood estimator(MLE),modified MLE,modified unbiased estimator and modified best linear unbiased estimator(BLUE)for the Power-law distribution will be respectively studied under SRS and RSS.In addition,these estimators using an RSS version based on the order statistic that maximizes the Fisher information number for a fixed set size,will be studied.The simulation results show that these estimators under RSS are significantly more efficient than the ones under SRS.

关 键 词：排序集抽样 极大似然估计 修正极大似然估计 修正最优线性无偏估计 

分 类 号：O212.1[理学—概率论与数理统计]