调整经验欧氏似然及其性质

发布时间：2018-04-15 06:20

本文选题：调整经验欧氏似然 + 置信区间　；参考：《广西师范大学》2011年硕士论文

【摘要】：经验似然是近年来非常流行的非参数统计方法之一,它在许多领域都展示了其较强的魅力,得到了较为成功地应用,如计量经济学、生物医学和市场调查等领域。是目前统计理论和应用研究里热门的研究课题之一。本论文在对前人已有研究成果进行综合分析的基础上,主要考察调整的经验欧氏似然。经验似然函数是由Owen(1988)最早提出的,Qin and Lawless(1994)将其方法引入到较为一般的半参数模型中。经验欧氏似然是用欧氏距离代替经验似然中似然距离而得到的一种非参数方法,它具有与经验似然完全类似的性质,因此可以看作是经验似然的一种推广版本。计划针对经验欧氏似然方法理论和应用上的一点不足之处,即凸包限制问题,对经验欧氏似然进行调整并对其性质加以讨论。论文主要借助Chen、Variyath和Abraham(2008)的调整经验似然思想,在半参数模型下,讨论调整经验欧氏似然函数的构造,参数估计(包括点估计和区间估计),分布函数的估计等问题,理论上给出了前述所得估计的极限性质。然后再从小样本方面,通过模拟对所得方法的优越性进行了比较。理论上我们发现,调整的经验欧氏似然与经验似然或经验欧氏似然有完全类似的性质；模拟结果显示,在某些情况下(如二维情况),由调整的经验欧氏似然所得的区间估计具有较好的覆盖率。更为重要的是,调整经验欧氏似然的思想和计算都比较简单。从实用角度看,具有较高的推广价值。本论文特色主要体现在以下几个方面： 1.对经验欧氏似然进行调整,得到了调整的经验欧氏似然比统计量,讨论该统计量以及其相应参数估计的渐近性质,如渐近分布,相合性等。这些成果是前人所没有讨论的,是完全新的成果。 2.本论文所得的调整经验欧氏似然计算简单,与没有调整的经验似然或经验欧氏似然相比,它没有0点必须落在估计函数g(x1,θ),…,g(xn,θ)内部的要求,对所有情况均有解存在,减少了计算的复杂性。 3.在某些情况下,由本文结论所得的估计的置信区域的覆盖率要高于已有的估计方法所对应的置信区域的覆盖率。 4.本论文结论可以丰富和完善经验欧氏似然的理论,为实际应用工作者提供简便可行的工具。
[Abstract]:Empirical likelihood is one of the most popular non-parametric statistical methods in recent years. It has been applied successfully in many fields, such as econometrics, biomedicine and market research.At present, it is one of the hot research topics in statistical theory and application research.Based on the comprehensive analysis of the previous research results, this paper mainly investigates the adjusted empirical Euclidean likelihood (Euclidean likelihood).Empirical likelihood function (EMLF) was first proposed by Owen and Lawless 1994) and introduced into the general semi-parametric model.Empirical Euclidean likelihood (Euclidean likelihood) is a nonparametric method which uses Euclidean distance instead of Euclidean distance in empirical likelihood. It is completely similar to empirical likelihood, so it can be regarded as a generalized version of empirical likelihood.Aiming at one deficiency in the theory and application of empirical Euclidean likelihood (Euclidean likelihood), that is, convex hull restriction problem, the paper adjusts the empirical Euclidean likelihood and discusses its properties.In this paper, with the help of Chenan Variyath and Abrahamian 2008, we discuss the construction of adjusted empirical Euclidean likelihood function, parameter estimation (including point estimation and interval estimation, estimation of distribution function, etc.) under the semi-parametric model.The limit properties of the above obtained estimates are given theoretically.Then, the advantages of the method are compared by simulation from small samples.Theoretically, we find that the adjusted empirical Euclidean likelihood is completely similar to the empirical Euclidean likelihood or empirical Euclidean likelihood.In some cases, such as two-dimensional case, the interval estimates obtained from the adjusted empirical Euclidean likelihood have better coverage.More importantly, the idea and calculation of adjusting empirical Euclidean likelihood are relatively simple.From a practical point of view, has a higher promotion value.The main features of this paper are as follows:1.By adjusting the empirical Euclidean likelihood, the adjusted empirical Euclidean likelihood ratio statistic is obtained. The asymptotic properties of the statistic and its corresponding parameter estimates, such as asymptotic distribution and consistency, are discussed.These achievements have not been discussed before, they are completely new.2.The modified empirical Euclidean likelihood obtained in this paper is simple to calculate. Compared with the empirical likelihood without adjustment or empirical Euclidean likelihood, it does not have zero points which must fall on the estimation function gnx1, 胃, 鈥he internal requirement of gn, 胃) has a solution for all cases and reduces the computational complexity.3.In some cases, the coverage of the estimated confidence regions is higher than that of the confidence regions corresponding to the existing estimation methods.4.The conclusion of this paper can enrich and perfect the empirical Euclidean likelihood theory and provide a simple and feasible tool for practical application workers.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：O212.7

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