Cramer-Rao下界的扩充解释及其对帕累托分布参数倒数的估计  

The Expanded Interpretation of Cramer-Rao Lower Bound and its Estimation of the Reciprocal of Pareto Distribution Parameters

作　　者：陶玉婷 赵海峰 TAO Yu-ting;ZHAO Hai-feng(Jinling Institute of Technology,Nanjing 211169,China;Jiangsu Hoperun Software Co.Ltd.,Nanjing 210012,China;Information Analysis Engineering Research Center of Jiangsu Province,Nanjing 211169,China)

机构地区：[1]金陵科技学院软件工程学院,江苏南京211169 [2]江苏润和软件股份有限公司,江苏南京210012 [3]江苏省信息分析工程研究中心,江苏南京211169

出　　处：《金陵科技学院学报》2023年第2期1-8,共8页Journal of Jinling Institute of Technology

基　　金：江苏省高校自然科学研究重大项目(21KJA520001);江苏省国际科技合作项目(BZ2020069);金陵科技学院科研孵化项目(jit-fhxm-201911)。

摘　　要：Cramer-Rao下界是统计学中非常重要的下界,也是Fisher信息量的倒数。针对Cramer-Rao正则族成立的5个条件以及参数函数无偏估计的方差下限值,从微积分计算的角度对Cramer-Rao下界进行扩充解释,证明了帕累托分布参数倒数的最大似然估计能达到Cramer-Rao下界,并给出了该参数倒数的另一个无偏估计。结果表明只有在无偏估计与参数本身无关的情况下,该估计的方差下限值才是Cramer-Rao下界。Cramer-Rao lower bound(CRLB)is a significant lower bound in statistics,which is the reciprocal of Fisher information.Pinpointing at the five conditions satisfied by Cramer-Rao regular family and the lower bound value for the variance of unbiased parameter s function,this paper provides the expanded interpretation of CRLB from the perspective of calculus calculation.It proves that the maximum likelihood estimation of the reciprocal of Pareto distribution parameter could attain CRLB.In addition,it offers another unbiased estimator for the reciprocal.The results show that the unbiased estimator s variance could attain CRLB,only if the estimator is irrelevant to the parameter itself.

关 键 词：CRAMER-RAO下界 FISHER信息量 Cramer-Rao正则族 帕累托分布 最大似然估计 无偏估计 

分 类 号：O212.1[理学—概率论与数理统计]