Improved robust Bayes estimators of the error variance in linear models

Details Improved robust Bayes estimators of the error variance in linear models Improved robust Bayes estimators of the error variance in linear models

2010-04-01

arxiv.org/abs/1004.0234v2

Mathematics

Statistics Theory

11 pages

Scientific paper

We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of Gaussians including the particularly important case of the multivariate-t distribution. Under Stein's loss, we construct a class of estimators that improve on the usual best unbiased (and best equivariant) estimator. Our class has the interesting double robustness property of being simultaneously generalized Bayes (for the same generalized prior) and minimax over the entire class of scale mixture of Gaussian distributions.

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