几类连续分布的E-Bayes估计

发布时间：2018-01-11 02:11

本文关键词：几类连续分布的E-Bayes估计　出处：《上海师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：Bayes统计,特别是Bayes统计计算,近年来取得重大进展,是当今统计学发展最快的分支之一,已经成为当今统计学的重要组成部分。自从Lindley等提出多层先验分布的思想以来,多层Bayes方法在参数估计方面取得了一些进展。但用多层Bayes方法得到的结果一般都要涉及积分的计算,虽然有MCMC(Markov Chain Monte Carlo)等计算方法,但在有些问题的应用上还是不太方便,这在一定程度上制约了多层Bayes方法的应用。中国学者韩明于2004年提出了一种修正的Bayes估计法——“参数的E-Bayes估计法”,从而适当的解决了这一难题。本文就是在Bayes估计的基础上,研究了Burr分布、Laplace分布和Rayleigh分布三种连续分布参数的E-Bayes估计,并通过数值模拟,来验证本文所研究的E-Bayes估计的合理性和优良性。首先在平方损失函数??(??,??)=(??-??)2和Q-对称熵损失函数??(??,??)=(???下利用共轭分布研究了Burr分布的E-Bayes估计和多层Bayes估计,并讨论了E-Bayes估计的性质,证明了其与多层Bayes估计的渐近相等性,同时给出了数值算例对两种估计进行比较,说明了Q-对称熵损失函数比平方损失函数具有更优越的性质。其次,在Q-对称熵损失函数下分别讨论了Laplace分布和Rayleigh分布尺度参数的多层Bayes估计和E-Bayes估计,并给出数值算例说明了两种估计在大样本下渐近相等的性质。最后得出结论,E-Bayes估计与多层Bayes估计渐近相等,但E-Bayes估计形式简单,实际应用更加方便。
[Abstract]:Bayes statistics, especially Bayes statistics, have made great progress in recent years and are one of the fastest growing branches of statistics. It has become an important part of statistics since Lindley et al proposed the idea of multilayer prior distribution. The multilayer Bayes method has made some progress in parameter estimation, but the results obtained by the multilayer Bayes method usually involve the calculation of integral. Although there are some calculation methods, such as MCMC(Markov Chain Monte method, it is not very convenient to apply some problems. In 2004, Han Ming, a Chinese scholar, proposed a modified Bayes estimation method, called "parameter E-Bayes estimation method". In this paper, we study the Burr distribution on the basis of Bayes estimation. E-Bayes estimation of three kinds of continuous distribution parameters of Laplace distribution and Rayleigh distribution, and numerical simulation. To verify the reasonableness and excellence of the E-Bayes estimator studied in this paper. ? What? ? ,? ? What? ? -? ? Q-symmetric entropy loss function? ? What? ? ,? ? What? ? ? Based on the conjugate distribution, we study the E-Bayes estimation and multilayer Bayes estimator of Burr distribution, and discuss the properties of E-Bayes estimator. It is proved that it is asymptotically equal to the multilevel Bayes estimator. A numerical example is given to compare the two estimators. It is proved that the Q-symmetric entropy loss function is superior to the square loss function. Under the Q-symmetric entropy loss function, the multilayer Bayes estimation and the E-Bayes estimation of the scale parameters of the Laplace distribution and the Rayleigh distribution are discussed, respectively. Numerical examples are given to illustrate the asymptotic equality of the two estimators under large samples. Finally, it is concluded that the E-Bayes estimator is asymptotically equal to the multilevel Bayes estimator. But E-Bayes estimation form is simple and practical application is more convenient.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.8

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