本文關(guān)鍵詞： 刀切法 經(jīng)驗(yàn)似然 秩集抽樣樣本 總體均值 兩總體均值差異 總體分位數(shù) 兩總體分位數(shù)差異　出處：《東北師范大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：秩集抽樣方法是McIntyre G A在澳大利亞研究牧草產(chǎn)量時(shí)首次提出來的一種抽樣方法.他認(rèn)為在相同的樣本容量下,基于秩集抽樣方法得到的樣本相對(duì)于基于簡(jiǎn)單隨機(jī)抽樣方法得到的樣本來說,常�？梢蕴峁└嗟男畔�,做出更有效的推斷.而經(jīng)驗(yàn)似然是Owen A B提出的一種可以對(duì)總體分布族未知的數(shù)據(jù)像參數(shù)似然方法那樣做統(tǒng)計(jì)推斷的非參數(shù)方法.它具有很多與參數(shù)似然方法類似的優(yōu)良性質(zhì),且該方法得到的置信區(qū)域的形狀是由數(shù)據(jù)決定的。本文將經(jīng)驗(yàn)似然方法應(yīng)用到秩集抽樣樣本,得到了如下結(jié)果：1.在第二章中,為了解決基于非平衡秩集抽樣樣本的檢驗(yàn)和估計(jì)問題,我們基于Jing B Y, Yuan J Q, Zhou W在2009年提出的刀切經(jīng)驗(yàn)似然方法,提出了一種適用于平衡和非平衡秩集抽樣的名為RSS-JEL的新方法.并用該方法得到了總體均值和兩總體均值差異基于平衡和非平衡秩集抽樣樣本的經(jīng)驗(yàn)對(duì)數(shù)似然比統(tǒng)計(jì)量在原假設(shè)為真的情況下的漸近分布為標(biāo)準(zhǔn)卡方分布。2.在第三章,考慮到分位數(shù)與Liu T Q, Lin N, Zhang B X在2009年所發(fā)表的論文中由估計(jì)方程所定義的參數(shù)在數(shù)學(xué)處理上有比較大的不同,本章應(yīng)用Chen和Hall在1993年提出的光滑經(jīng)驗(yàn)似然方法,給出了總體分位數(shù)和兩總體分位數(shù)差異基于平衡秩集抽樣樣本的光滑經(jīng)驗(yàn)似然置信區(qū)間.在此方法下分位數(shù)和分位數(shù)差異基于平衡秩集抽樣樣本的經(jīng)驗(yàn)對(duì)數(shù)似然比統(tǒng)計(jì)量在原假設(shè)為真的情況下的漸近分布是標(biāo)準(zhǔn)卡方分布。3.在第四章,我們應(yīng)用第二章提出的方法RSS-JEL將第三章的結(jié)果推廣到了非平衡秩集抽樣樣本情形。4.本文所給的結(jié)果不需要現(xiàn)有的基于秩的非參數(shù)方法所需要的任何易于去掉的條件.例如要求完美排序,或者要求兩組秩集抽樣有相同的排序方案,或者要求兩個(gè)總體的分布同屬于一個(gè)位移參數(shù)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.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O212.1

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本文編號(hào)：1493072