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Why is regression so commonly used if the OLS estimator for the vector of regression coefficients is inadmissible under the squared error loss function? Is it because of its historical popularity or the ease of computation or some other practical reason?

Is there some method that dominates the OLS estimator for the regression coefficients, assuming the standard multiple linear regression model?

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    $\begingroup$ Could you please provide a link for the inadmissibility claim? $\endgroup$ – JohnK Dec 30 '15 at 21:37
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I'm not familiar with the inadmissibility claim... but intuitively, my thought is that an estimator being unbiased is critical. In a world where most people do not understand statistical uncertainty and precision, I think that the MLE/OLS estimator is more appropriate and makes more sense when reporting estimates.

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    $\begingroup$ I think the OP refers to James-Stein estimator but I am not very familiar with the topic. $\endgroup$ – JohnK Dec 30 '15 at 22:01
  • $\begingroup$ I agree, if your loss function really penalizes bias, but if your loss function is squared error loss, a consistent estimator with low MSE might be better than an unbiased estimator with high MSE. $\endgroup$ – frelk Jan 19 '16 at 2:38
  • $\begingroup$ Correct, but what is the context for the problem? Are you talking about statistical rigor or practical applications? $\endgroup$ – Matt Brems Jan 19 '16 at 3:14

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