**I** recently came across this paper written by three philosophers of Science, attempting to set the Stein paradox in a philosophical light. Given my past involvement, I was obviously interested about which new perspective could be proposed, close to sixty years after Stein (1956). Paper that we should actually celebrate next year! However, when reading the document, I did not find a significantly innovative approach to the phenomenon…

The paper does not start in the best possible light since it seems to justify the use of a sample mean through maximum likelihood estimation, which only is the case for a limited number of probability distributions (including the Normal distribution, which may be an implicit assumption). For instance, when the data is Student’s t, the MLE is not the sample mean, no matter how shocking that might sounds! (And while this is a minor issue, results about the Stein effect taking place in non-normal settings appear much earlier than 1998. And earlier than in my dissertation. See, e.g., Berger and Bock (1975). Or in Brandwein and Strawderman (1978).)

While the linear regression explanation for the Stein effect is already exposed in Steve Stigler’s Neyman Lecture, I still have difficulties with the argument in that for instance we do not know the value of the parameter, which makes the regression and the inverse regression of parameter means over Gaussian observations mere concepts and nothing practical. (Except for the interesting result that two observations make both regressions coincide.) And it does not seem at all intuitive (to me) that imposing a constraint should improve the efficiency of a maximisation program… Continue reading