【摘要】：在很多情況下,排序集抽樣(Rankedset sapling,簡稱RSS)是一種相對于簡單隨機(jī)抽樣(Simple ranked sampling,簡稱SRS)更加有效的數(shù)據(jù)收集方式,包含信息量也比SRS多,因此從上世紀(jì)開始,RSS這種抽樣方式在統(tǒng)計(jì)推斷方面應(yīng)用廣泛.但是RSS也有它自身的缺點(diǎn),比如出現(xiàn)排序錯誤的可能性較大,為了降低排序錯誤率,emphAl-saleh提出了修正的RSS,即:動態(tài)極端排序集抽樣(Moving extreme ranκked set sampling,簡稱MERSS),并在這個抽樣方式下研究指數(shù)分布的參數(shù)λ的極大似然估計(jì)(Maximum likelihood estimation,簡稱MLE)的性質(zhì),并給定了 λ的修正極大似然估計(jì)的無偏估計(jì)的形式.于2007年Al saleh又研究MERSS下二維正態(tài)分布的參數(shù)估計(jì)問題.基于上述的研究,本文討論Morgenstern型二維指數(shù)分布在MERSS這種抽樣方式下的研究變量Y的參數(shù)λ的估計(jì)問題.在之前的研究中,有Chacko研究過Morgenstern型二維指數(shù)分布在RSS下的參數(shù)估計(jì)問題.本文主要研究內(nèi)容是在MERSS下,Morgenstern型二維指數(shù)分布在輔助變量X的參數(shù)θ已知的情形下關(guān)于研究變量Y的參數(shù)λ的估計(jì)問題.第一部分介紹前人的研究成果,并詳細(xì)介紹RSS及MRSS的抽樣方法、第二部分為準(zhǔn)備工作,主要介紹Morgernstern型二維指數(shù)分布的密度函數(shù)、研究變量Y在輔助變量X已知時的分布密度函數(shù),給出排序相依變量的均值及方差,并證明研究變量Y的均值為其參數(shù)λ的無偏估計(jì).第三部分主要探究參數(shù)θ已知的情況下參數(shù)λ的MLE估計(jì)及其性質(zhì),通過研究參數(shù)λ的Fisher信息量說明其極大似然估計(jì)效果較好,并證明參數(shù)λ的修正MLE是無偏估計(jì).
[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.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

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本文編號：2336726