## Bayesian propaganda?

“The question is about frequentist approach. Bayesian is admissable [sic] only by wrong definition as it starts with the assumption that the prior is the correct pre-information. James-Stein beats OLS without assumptions. If there is an admissable[sic]frequentist estimator then it will correspond to a true objective prior.”

**I** had a wee bit of a (minor, very minor!) communication problem on X validated, about a question on the existence of admissible estimators of the linear regression coefficient in multiple dimensions, under squared error loss. When I first replied that all Bayes estimators with finite risk were *de facto* admissible, I got the above reply, which clearly misses the point, and as I had edited the OP question to include more tags, the edited version was reverted with a comment about Bayesian propaganda! This is rather funny, if not hilarious, as (a) Bayes estimators are indeed admissible in the classical or frequentist sense—I actually fail to see a definition of admissibility in the Bayesian sense—and (b) the complete class theorems of Wald, Stein, and others (like Jack Kiefer, Larry Brown, and Jim Berger) come from the frequentist quest for best estimator(s). To make my point clearer, I also reproduced in my answer the Stein’s necessary and sufficient condition for admissibility from my book but it did not help, as the theorem was “too complex for [the OP] to understand”, which shows *in fine* the point of reading textbooks!

April 20, 2015 at 12:38 am

That sneaky Bayesian spin-meister Wald, naming the class of admissible estimators ‘Bayes estimators’ just because the class contains all and only procedures (or limits of procedures) that minimize posterior expected loss!

April 20, 2015 at 7:00 pm

I also like the notion that an admissible frequentist estimator corresponds to a “true objective prior”. Objectivity is in the eye of the beholder.

April 21, 2015 at 2:33 pm

“true objective prior” makes my teeth hurt!

April 21, 2015 at 3:26 pm

my teeth rattled so much that they all but fell..!