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We deal with the expectation of random functionals with the Dirichlet process, using Sethuraman's representation. As an application of this expectation, we obtain the Bayes estimates of estimable para...meters with the squared error loss based on the Dirichlet prior process. From the Bayes estimates, we obtain the limits of Bayes estimates, which may be used for the non-Bayesian inference. We see the differences of the limits of Bayes estimates from the corresponding $ U $-statistics and the $ V $-statistics, for five estimable parameters of degree two.show more
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