I read a lot of sources concerning stein's estimator and James-Stein estimator. Unfortunately, a lot of sources do not write the correct formulas of each estimator. And so I am now confused!!

Kindly, can someone explain me in details the difference between Stein's and James-Stein estimators.

1) How James-Stein (1962) estimator differs from Stein's estimator(1955).*

2) Why James-Stein is developed in order to improve the Stein's estimator? So what are the disadvantages of Stein's estimator?

3) What are the correct formulas of each one?

4) Why Stein's estimator and James-Stein estimator are considered as shrinkage estimators?

Any brief explanation will be very appreciated!

  • $\begingroup$ Try contacting Prof. Emeritus Stein statistics.stanford.edu/people/charles-stein . Note that xxx = ord , which must be for anti-SPAM purposes. $\endgroup$ Jun 17 '15 at 11:33
  • $\begingroup$ In answer to a question in a no longer visible comment, Prof. Stein is still alive and living nearby Stanford. He only occasionally comes into the Statistics Department at Stanford, and it's not clear how frequently he checks email, so you should probably be patient. $\endgroup$ Jun 17 '15 at 15:50

I don't think there is a difference. Stein's result is to show inadmissibility of the mean in the case of multivariate normal. James-Stein developed the estimator for quadratic loss. The James-Stein estimator is sometimes called the Stein's estimator.

  • $\begingroup$ So Stein's estimator results in 1956 did not depend on a specific loss function? $\endgroup$
    – Christina
    May 27 '15 at 23:12
  • $\begingroup$ See section 1.4 and 1.5 of ieor.berkeley.edu/~kete/uploads/1/2/4/0/12408873/js.pdf $\endgroup$
    – Sid
    May 28 '15 at 0:32
  • $\begingroup$ Ja, but I am afraid if what he wrote is correct or not. However how he found the formula of James-Stein in section 1.7? because in the original article james didn't exhibit this formula. he simply explain the phenomenon of stein but in more general case. what is your opinion :) $\endgroup$
    – Christina
    May 28 '15 at 9:42

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