本文選題：排序集抽樣　切入點(diǎn)：對(duì)稱分布　出處：《華中師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：當(dāng)樣本個(gè)體較易排序且花費(fèi)較少時(shí),相較于簡單隨機(jī)抽樣(SRS),排序集抽樣(RSS)是一種更為精確有效的抽樣手段,它常結(jié)合一些傳統(tǒng)優(yōu)良的估計(jì)方法來估計(jì)總體均值或總體方差。在平衡的配置下,RSS比SRS的估計(jì)效率更高,而在某些非平衡的配置下,其估計(jì)效率比平衡配置下的RSS又有所提高。當(dāng)總體分布是對(duì)稱分布的情形時(shí),Kaur,Patil and Taillie (2000)給出了估計(jì)總體均值的最優(yōu)配置(方便表示簡稱KPT配置),該配置僅抽取中位數(shù)統(tǒng)計(jì)量或者最大、最小次序統(tǒng)計(jì)量進(jìn)行實(shí)際測量,其估計(jì)效率遠(yuǎn)優(yōu)于Neyman配置,而Neeraj Tiwari and Girja Shankar Pandey(2012)給出了估計(jì)總體均值的線性配置,認(rèn)為雖然KPT配置估計(jì)效率最高,但是KPT配置忽略了絕大部分的個(gè)體而只關(guān)注極少量的個(gè)體,其用于估計(jì)的樣本往往不夠充分。按照次序統(tǒng)計(jì)量的方差隨其秩變化而變化的情況,可將對(duì)稱分布分為兩類,分別為“山型”對(duì)稱分布和“U型”對(duì)稱分布,本文在KPT配置與線性配置的基礎(chǔ)上,針對(duì)此兩類對(duì)稱分布,提出了一個(gè)非線性配置模型,并在此配置下,給出了總體均值的最優(yōu)線性無偏估計(jì)量,同時(shí),也給出了與在簡單隨機(jī)抽樣下樣本均值的相對(duì)效率。最后,數(shù)值比較了各配置(平衡配置、Neyman配置、KPT配置、線性配置、非線性配置)下總體均值估計(jì)的相對(duì)效率。
[Abstract]:When sample individuals are easier to sort and cost less, sorting set sampling is a more accurate and effective sampling method than simple random sampling. It often combines some traditional estimation methods to estimate the mean or variance of the population. It is more efficient than SRS in balanced configuration, while in some non-equilibrium configurations, it is more efficient than SRS in some non-equilibrium configurations. Its estimation efficiency is higher than that of RSS in balanced configuration. When the population distribution is symmetric, the optimal configuration of estimating the mean of population is given. The optimal configuration of estimating the mean of the population is given (the KPT configuration is convenient for short, and the configuration only extracts the median position). Number statistics or maximum, The estimation efficiency of the minimum order statistic is much better than that of Neyman configuration, and Neeraj Tiwari and Girja Shankar Pandey 2012) gives the linear assignment of the total mean value, and considers that although KPT configuration is the most efficient, However, KPT configuration neglects the majority of individuals and only pays attention to a very small number of individuals, and the samples used for estimation are often inadequate. According to the variation of the variance of order statistics with its rank, the symmetric distribution can be divided into two categories. In this paper, on the basis of KPT collocation and linear collocation, a nonlinear collocation model is proposed for these two types of symmetric distributions. The optimal linear unbiased estimator of the population mean is given. At the same time, the relative efficiency between the sample mean and the sample average under simple random sampling is also given. Finally, various configurations (equilibrium collocation / Neyman collocation / KPT configuration, linear collocation) are numerically compared. The relative efficiency of population mean estimation under nonlinear collocation.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O212

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