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Are there any extensions of the James-Stein estimator for the case of dependent variables?

I've done numeric experiments with the James-Stein estimator on correlated normal variables (5-10 variables, correlation was about 0.3) and it still is better then Least Square estimator in 95% cases.

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    $\begingroup$ Don't forget - the criteria by which estimators are judged isn't, typically, "fraction of time better than this other estimator", but more akin to "long run average performance". So with your experiments, try calculating the average performance of J-S and LS over all your experiments instead. $\endgroup$ – jbowman May 24 '12 at 14:13
  • $\begingroup$ Theory does suggest that it will work though. $\endgroup$ – Michael Chernick May 24 '12 at 14:55
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The James-Stein estimator applies to any multivariate normal distribution of dimension 3 or more. So there is no extending it. It applies already as stated in the original theorem.

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