本文關(guān)鍵詞：幾類連續(xù)分布的E-Bayes估計　出處：《上海師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： E-Bayes估計 多層Bayes估計 損失函數(shù) 共軛先驗分布

【摘要】：Bayes統(tǒng)計,特別是Bayes統(tǒng)計計算,近年來取得重大進展,是當(dāng)今統(tǒng)計學(xué)發(fā)展最快的分支之一,已經(jīng)成為當(dāng)今統(tǒng)計學(xué)的重要組成部分。自從Lindley等提出多層先驗分布的思想以來,多層Bayes方法在參數(shù)估計方面取得了一些進展。但用多層Bayes方法得到的結(jié)果一般都要涉及積分的計算,雖然有MCMC(Markov Chain Monte Carlo)等計算方法,但在有些問題的應(yīng)用上還是不太方便,這在一定程度上制約了多層Bayes方法的應(yīng)用。中國學(xué)者韓明于2004年提出了一種修正的Bayes估計法——“參數(shù)的E-Bayes估計法”,從而適當(dāng)?shù)慕鉀Q了這一難題。本文就是在Bayes估計的基礎(chǔ)上,研究了Burr分布、Laplace分布和Rayleigh分布三種連續(xù)分布參數(shù)的E-Bayes估計,并通過數(shù)值模擬,來驗證本文所研究的E-Bayes估計的合理性和優(yōu)良性。首先在平方損失函數(shù)??(??,??)=(??-??)2和Q-對稱熵損失函數(shù)??(??,??)=(???下利用共軛分布研究了Burr分布的E-Bayes估計和多層Bayes估計,并討論了E-Bayes估計的性質(zhì),證明了其與多層Bayes估計的漸近相等性,同時給出了數(shù)值算例對兩種估計進行比較,說明了Q-對稱熵損失函數(shù)比平方損失函數(shù)具有更優(yōu)越的性質(zhì)。其次,在Q-對稱熵損失函數(shù)下分別討論了Laplace分布和Rayleigh分布尺度參數(shù)的多層Bayes估計和E-Bayes估計,并給出數(shù)值算例說明了兩種估計在大樣本下漸近相等的性質(zhì)。最后得出結(jié)論,E-Bayes估計與多層Bayes估計漸近相等,但E-Bayes估計形式簡單,實際應(yīng)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.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O212.8

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