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Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case
In this article, we consider two forms of shrinkage estimators of the me...
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Bayesian Shrinkage Estimation of Negative Multinomial Parameter Vectors
The negative multinomial distribution is a multivariate generalization o...
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RKL: a general, invariant Bayes solution for Neyman-Scott
Neyman-Scott is a classic example of an estimation problem with a partia...
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Simultaneous Inference for Multiple Proportions: A Multivariate Beta-Binomial Model
In this work, the construction of an m-dimensional Beta distribution fro...
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Nonparametric Empirical Bayes Estimation on Heterogeneous Data
The simultaneous estimation of many parameters η_i, based on a correspon...
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Use of Cross-validation Bayes Factors to Test Equality of Two Densities
We propose a non-parametric, two-sample Bayesian test for checking wheth...
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Bayes factors with (overly) informative priors
Priors in which a large number of parameters are specified to be indepen...
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Superiority of Bayes estimators over the MLE in high dimensional multinomial models and its implication for nonparametric Bayes theory
This article focuses on the performance of Bayes estimators, in comparison with the MLE, in multinomial models with a relatively large number of cells. The prior for the Bayes estimator is taken to be the conjugate Dirichlet, i.e., the multivariate Beta, with exchangeable distributions over the coordinates, including the non-informative uniform distribution. The choice of the multinomial is motivated by its many applications in business and industry, but also by its use in providing a simple nonparametric estimator of an unknown distribution. It is striking that the Bayes procedure outperforms the asymptotically efficient MLE over most of the parameter spaces for even moderately large dimensional parameter space and rather large sample sizes.
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