Bayes Convolution |
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| Authors: | Edwin R van den Heuvel Chris A J Klaassen |
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| Institution: | Institute for Business and Industrial Statistics, IBIS UvA BV, University of Amsterdam, The Netherlands.;IBIS UvA B. V. and Korteweg-de Vries Institute for Mathematics, University of Amsterdam, The Netherlands. E-mail: |
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| Abstract: | A general convolution theorem within a Bayesian framework is presented. Consider estimation of the Euclidean parameter θ by an estimator T within a parametric model. Let W be a prior distribution for θ and define G as the W -average of the distribution of T - θ under θ . In some cases, for any estimator T the distribution G can be written as a convolution G = K * L with K a distribution depending only on the model, i.e. on W and the distributions under θ of the observations. In such a Bayes convolution result optimal estimators exist, satisfying G = K . For location models we show that finite sample Bayes convolution results hold in the normal, loggamma and exponential case. Under regularity conditions we prove that normal and loggamma are the only smooth location cases. We also discuss relations with classical convolution theorems. |
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| Keywords: | Bayes Convolution Loggamma |
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