总体均值和分位数基于秩集抽样样本的经验似然推断

发布时间：2018-02-05 23:47

本文关键词： 刀切法经验似然秩集抽样样本总体均值两总体均值差异总体分位数两总体分位数差异　出处：《东北师范大学》2016年博士论文　论文类型：学位论文

【摘要】：秩集抽样方法是McIntyre G A在澳大利亚研究牧草产量时首次提出来的一种抽样方法.他认为在相同的样本容量下,基于秩集抽样方法得到的样本相对于基于简单随机抽样方法得到的样本来说,常常可以提供更多的信息,做出更有效的推断.而经验似然是Owen A B提出的一种可以对总体分布族未知的数据像参数似然方法那样做统计推断的非参数方法.它具有很多与参数似然方法类似的优良性质,且该方法得到的置信区域的形状是由数据决定的。本文将经验似然方法应用到秩集抽样样本,得到了如下结果：1.在第二章中,为了解决基于非平衡秩集抽样样本的检验和估计问题,我们基于Jing B Y, Yuan J Q, Zhou W在2009年提出的刀切经验似然方法,提出了一种适用于平衡和非平衡秩集抽样的名为RSS-JEL的新方法.并用该方法得到了总体均值和两总体均值差异基于平衡和非平衡秩集抽样样本的经验对数似然比统计量在原假设为真的情况下的渐近分布为标准卡方分布。2.在第三章,考虑到分位数与Liu T Q, Lin N, Zhang B X在2009年所发表的论文中由估计方程所定义的参数在数学处理上有比较大的不同,本章应用Chen和Hall在1993年提出的光滑经验似然方法,给出了总体分位数和两总体分位数差异基于平衡秩集抽样样本的光滑经验似然置信区间.在此方法下分位数和分位数差异基于平衡秩集抽样样本的经验对数似然比统计量在原假设为真的情况下的渐近分布是标准卡方分布。3.在第四章,我们应用第二章提出的方法RSS-JEL将第三章的结果推广到了非平衡秩集抽样样本情形。4.本文所给的结果不需要现有的基于秩的非参数方法所需要的任何易于去掉的条件.例如要求完美排序,或者要求两组秩集抽样有相同的排序方案,或者要求两个总体的分布同属于一个位移参数族。
[Abstract]:Rank set sampling is the first sampling method proposed by McIntyre G A in Australia when studying forage yield. He thinks that under the same sample size. Samples based on rank set sampling can often provide more information than those based on simple random sampling. Make a more effective inference. Experience is likely to be Owen A. B is a nonparametric method which can infer the unknown data of the population distribution family like the parametric likelihood method. It has many good properties similar to the parametric likelihood method. The shape of the confidence region obtained by this method is determined by the data. In this paper, the empirical likelihood method is applied to the rank set sampling samples, and the following results are obtained: 1. In Chapter 2. In order to solve the problem of testing and estimating samples based on nonequilibrium rank sets, we based on Jing B Y, Yuan J Q. In 2009, Zhou W put forward the empirical likelihood method of knife cutting. In this paper, a new method called RSS-JEL, which is suitable for balanced and non-equilibrium rank set sampling, is proposed. By using this method, the experience of sampling samples based on equilibrium and non-equilibrium rank sets is obtained. The asymptotic distribution of logarithmic likelihood ratio statistics is standard chi-square distribution. Considering that the quantiles are quite different from the parameters defined by the estimation equation in the paper published in 2009 by Liu T Q, Lin N, Zhang B X in mathematical processing. This chapter applies the smooth empirical likelihood method proposed by Chen and Hall in 1993. In this paper, the smooth empirical likelihood confidence interval of population quantile and two-population quantile difference based on the sample sample of balanced rank set is given. In this method, the difference of quantile and quantile is based on the empirical logarithmic likelihood of sample of balanced rank set sampling. The asymptotic distribution of the ratio statistic is standard chi-square distribution. 3. In Chapter 4th, the asymptotic distribution of the ratio statistic is assumed to be true. We apply the method proposed in Chapter 2, RSS-JEL, to extend the results of Chapter 3 to the sample case of nonequilibrium rank set sampling. 4. The results given in this paper do not require the existing rank based nonparametric methods. Any condition that is easy to remove, such as requiring a perfect sort. Either the two groups of rank set sampling have the same ranking scheme, or the distribution of the two populations belong to the same displacement parameter family.
【学位授予单位】：东北师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.1

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