排序集抽样下以称分布总体均值估计的非线性配置

发布时间：2018-03-18 20:30

本文选题：排序集抽样　切入点：对称分布　出处：《华中师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：当样本个体较易排序且花费较少时,相较于简单随机抽样(SRS),排序集抽样(RSS)是一种更为精确有效的抽样手段,它常结合一些传统优良的估计方法来估计总体均值或总体方差。在平衡的配置下,RSS比SRS的估计效率更高,而在某些非平衡的配置下,其估计效率比平衡配置下的RSS又有所提高。当总体分布是对称分布的情形时,Kaur,Patil and Taillie (2000)给出了估计总体均值的最优配置(方便表示简称KPT配置),该配置仅抽取中位数统计量或者最大、最小次序统计量进行实际测量,其估计效率远优于Neyman配置,而Neeraj Tiwari and Girja Shankar Pandey(2012)给出了估计总体均值的线性配置,认为虽然KPT配置估计效率最高,但是KPT配置忽略了绝大部分的个体而只关注极少量的个体,其用于估计的样本往往不够充分。按照次序统计量的方差随其秩变化而变化的情况,可将对称分布分为两类,分别为“山型”对称分布和“U型”对称分布,本文在KPT配置与线性配置的基础上,针对此两类对称分布,提出了一个非线性配置模型,并在此配置下,给出了总体均值的最优线性无偏估计量,同时,也给出了与在简单随机抽样下样本均值的相对效率。最后,数值比较了各配置(平衡配置、Neyman配置、KPT配置、线性配置、非线性配置)下总体均值估计的相对效率。
[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.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212

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