Empirical bayes estimation of the mean in a multivariate normal distribution |
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Authors: | S. James Press John E. Rolph |
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Affiliation: | 1. University of California , Riverside, CA, 92521;2. The Rand Corporation , Santa Monica, CA, 90406 |
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Abstract: | We consider the problem of estimating the mean vector of a multivariate normal distribution under a variety of assumed structures among the parameters of the sampling and prior distributions. We adopt a pragmatic approach. We adopt distributional familites, assess hyperparmeters, and adopt patterned mean and coveariance structures when it is relatively simple to do so; alternatively, we use the sample data to estimate hyperparameters of prior distributions when assessment is a formidable task; such as the task of assessing parameters of multidimensional problems. James-Stein-like estimators are found to result. In some cases, we've been abl to show that the estimators proposed uniformly dominate the MLE's when measured with respect to quadratic loss functions. |
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Keywords: | Empirical Bayes Estimation Multivariate Bayes Multivariate normal |
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