动态极端排序集抽样下Morgenstern型二维指数分布参数估计
发布时间：2018-11-16 21:48
【摘要】：在很多情况下,排序集抽样(Rankedset sapling,简称RSS)是一种相对于简单随机抽样(Simple ranked sampling,简称SRS)更加有效的数据收集方式,包含信息量也比SRS多,因此从上世纪开始,RSS这种抽样方式在统计推断方面应用广泛.但是RSS也有它自身的缺点,比如出现排序错误的可能性较大,为了降低排序错误率,emphAl-saleh提出了修正的RSS,即:动态极端排序集抽样(Moving extreme ranκked set sampling,简称MERSS),并在这个抽样方式下研究指数分布的参数λ的极大似然估计(Maximum likelihood estimation,简称MLE)的性质,并给定了 λ的修正极大似然估计的无偏估计的形式.于2007年Al saleh又研究MERSS下二维正态分布的参数估计问题.基于上述的研究,本文讨论Morgenstern型二维指数分布在MERSS这种抽样方式下的研究变量Y的参数λ的估计问题.在之前的研究中,有Chacko研究过Morgenstern型二维指数分布在RSS下的参数估计问题.本文主要研究内容是在MERSS下,Morgenstern型二维指数分布在辅助变量X的参数θ已知的情形下关于研究变量Y的参数λ的估计问题.第一部分介绍前人的研究成果,并详细介绍RSS及MRSS的抽样方法、第二部分为准备工作,主要介绍Morgernstern型二维指数分布的密度函数、研究变量Y在辅助变量X已知时的分布密度函数,给出排序相依变量的均值及方差,并证明研究变量Y的均值为其参数λ的无偏估计.第三部分主要探究参数θ已知的情况下参数λ的MLE估计及其性质,通过研究参数λ的Fisher信息量说明其极大似然估计效果较好,并证明参数λ的修正MLE是无偏估计.
[Abstract]:In many cases, sorting set sampling (Rankedset sapling, (RSS) is a more efficient way to collect data than simple random sampling (Simple ranked sampling, (SRS), and contains more information than SRS, so it began in the last century. RSS sampling is widely used in statistical inference. However, RSS also has its own disadvantages, such as the possibility of a sort error. In order to reduce the sorting error rate, emphAl-saleh proposed a modified RSS, that is, dynamic extreme sort set sampling (Moving extreme ran 魏 ked set sampling, for MERSS),. The properties of the maximum likelihood estimation (Maximum likelihood estimation,) of the parameter 位 of exponential distribution are studied in this sampling method, and the unbiased form of the modified maximum likelihood estimate of 位 is given. In 2007, Al saleh also studied the parameter estimation of two-dimensional normal distribution under MERSS. Based on the above research, this paper discusses the estimation of parameter 位 of Morgenstern type two-dimensional exponential distribution under MERSS sampling. In previous studies, Chacko has studied the parameter estimation problem of Morgenstern type two-dimensional exponential distribution under RSS. The main content of this paper is to study the estimation of parameter 位 of variable Y under MERSS, where the parameter 胃 of the auxiliary variable X is known. The first part introduces the previous research results, and introduces the sampling methods of RSS and MRSS in detail. The second part is the preparatory work, mainly introduces the density function of the Morgernstern type two-dimensional exponential distribution. The distribution density function of the variable Y is studied when the auxiliary variable X is known. The mean value and variance of the ordered dependent variable are given, and it is proved that the mean value of the studied variable Y is the unbiased estimate of its parameter 位. The third part mainly discusses the MLE estimation and its properties of parameter 位 when the parameter 胃 is known, and proves that the modified MLE of parameter 位 is an unbiased estimate by studying the Fisher information of parameter 位.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
本文编号：2336726
[Abstract]:In many cases, sorting set sampling (Rankedset sapling, (RSS) is a more efficient way to collect data than simple random sampling (Simple ranked sampling, (SRS), and contains more information than SRS, so it began in the last century. RSS sampling is widely used in statistical inference. However, RSS also has its own disadvantages, such as the possibility of a sort error. In order to reduce the sorting error rate, emphAl-saleh proposed a modified RSS, that is, dynamic extreme sort set sampling (Moving extreme ran 魏 ked set sampling, for MERSS),. The properties of the maximum likelihood estimation (Maximum likelihood estimation,) of the parameter 位 of exponential distribution are studied in this sampling method, and the unbiased form of the modified maximum likelihood estimate of 位 is given. In 2007, Al saleh also studied the parameter estimation of two-dimensional normal distribution under MERSS. Based on the above research, this paper discusses the estimation of parameter 位 of Morgenstern type two-dimensional exponential distribution under MERSS sampling. In previous studies, Chacko has studied the parameter estimation problem of Morgenstern type two-dimensional exponential distribution under RSS. The main content of this paper is to study the estimation of parameter 位 of variable Y under MERSS, where the parameter 胃 of the auxiliary variable X is known. The first part introduces the previous research results, and introduces the sampling methods of RSS and MRSS in detail. The second part is the preparatory work, mainly introduces the density function of the Morgernstern type two-dimensional exponential distribution. The distribution density function of the variable Y is studied when the auxiliary variable X is known. The mean value and variance of the ordered dependent variable are given, and it is proved that the mean value of the studied variable Y is the unbiased estimate of its parameter 位. The third part mainly discusses the MLE estimation and its properties of parameter 位 when the parameter 胃 is known, and proves that the modified MLE of parameter 位 is an unbiased estimate by studying the Fisher information of parameter 位.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
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