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http://ir.lib.ncu.edu.tw/handle/987654321/27796

Title:  Posterior robustness in simultaneous estimation problem with exchangeable contaminated priors 
Authors:  Liu,YH;Yang,MC 
Contributors:  統計研究所 
Keywords:  BAYESIANANALYSIS;RANGES;SENSITIVITY 
Date:  1997 
Issue Date:  20100629 19:33:48 (UTC+8) 
Publisher:  中央大學 
Abstract:  Let X1,...,Xp be independent random variables with densities f(i)(x(i)\theta(i)), i = 1,...,p. Suppose that theta(1),...,theta(p) are exchangeable random variables. In this paper we consider the Bayesian robustness or posterior sensitivity analysis with respect to the class of epsiloncontaminated prior distributions Gamma(AM)={(1epsilon)pi(0)+epsilon q: q is an element of(LAM)}, where LAM consists of all the exchangeable distributions on (theta(1),...,theta(p)) and for each distribution in LAM which can be expressed as a mixture of product of i.i.d. distributions. Most of the previous studies on posterior sensitivity analysis focus on a onedimensional parameter space, and the posterior quantities considered in those analyses are the posterior probability of a subset of the parameter space, the posterior mean, and the posterior variance. The loss function is usually not taken into consideration, or if it is, only the zeroone or squared error loss is considered. It is worthwhile to consider other loss functions and other interesting posterior quantities, which are the goals of the paper. Under the weighted squared error loss L(theta, delta)=Sigma(i=1)(p) w(i)(theta(i))(theta(i)delta(i))(2), we study the posterior sensitivity of the Bayes action, the posterior expected loss and some interested posterior quantities with respect to the class Gamma(AM). By using the de Finetti mixture representation of exchangeable random variables, the problem of finding the range of each component of the Bayes action over the class Gamma(AM) can be reduced to a much smaller class of distributions with support at at most p points. The range of other posterior quantities can also be obtained in a similar way. One example for simultaneous estimation of independent Poisson means is given. In this example we compute the ranges of Bayes action and discuss their posterior robustness issues. (C) 1997 Elsevier Science B.V. 
Relation:  JOURNAL OF STATISTICAL PLANNING AND INFERENCE 
Appears in Collections:  [統計研究所] 期刊論文

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