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The Comparison between Bayes Estimator and Shrinkage Estimation in the Two-parameter Exponential Distribution under Censorship

Author: Wang
Tutor: WangLiChun
School: Beijing Jiaotong University
Course: Probability Theory and Mathematical Statistics
Keywords: Two-parameter exponential distribution Bayes estimator typeⅡcensorship random censorship shrinkage estimation conjugate prior
CLC: O212.8
Type: Master's thesis
Year: 2010
Downloads: 38
Quote: 0
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Abstract


In this paper we discuss the scale parameter estimation problem of the two-parameter exponential distribution given location parameter under the typeⅡcensorship and random censorship. We show the Bayes estimator of the scale parameter with conjugate prior can be shrinkage estimation with the formθBE=aθ+bEθ, whereθis an unbiased estimator depending on samples and Eθis the expectation of the prior distribution g(θ).When we use the squared loss function, a+b=1.When we use the weighted squared loss function and r=1,then a+b=1; if r>1,then a+b<1. Comparing the two kinds of estimators, we know that the Bayes estimator is better than all the shrinkage estimators with form p=k(?)+(1-k)Eθ.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > Bayesian statistics
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