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SUMMARY:Charles Stein's 1956 inadmissibility paper - Larry Brown\, Statist
 ics Department\, University of Pennsylvania
DTSTART:20081016T160000Z
DTEND:20081016T170000Z
UID:TALK14652@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:Just over 50 years ago Stein published a startling statistical
  result. (Stein (1956).) When three or more normal means are to be estimat
 ed the sample mean is not an admissible estimator. It is better to 'shrink
 ' towards the origin\, or some other predetermined point.  At first this f
 act appeared to many as a mathematical peculiarity\, with no particular pr
 actical significance. Publication five years later of the James-Stein (196
 1) estimator demonstrated that the difference in performance could be quit
 e substantial between the sample mean and a suitable shrinkage estimator. 
 It\nhas become understood in the intervening decades how this minimax surp
 rise is intimately related to a variety of other practical statistical met
 hodologies and its principles applicable in a wide range of practical\nset
 tings.\n        \nStein's original paper included a geometrical explanatio
 n as to why such a paradoxical result is inevitable when estimating suffic
 iently many separate means\, as well a relatively simple proof that 3 is s
 ufficiently many. I'll supplement his geometric argument with a simple geo
 metric diagram and then sketch his proof. I can also remark about several 
 generalizations (Brown (1966)) of this proof that show this abnormal resul
 t is not only a result about the normal distribution and squared error los
 s (as some statisticians at the time had suspected).\n        \nI don't sp
 ecifically plan on discussing any further technicalities\, but if time per
 mits I can sketch where this seminal paper has led\, including especially 
 James-Stein (1961)\, mentioned above\, and Brown (1971)\nwhich attempts to
  show that there are several related mathematical situations where 3>>2.\n
     \n[Incidentally\, my Kuwait Lecture on Tuesday provides a specific ill
 ustration of how shrinkage ideas can be used in high dimensional data sett
 ings.]\n\nStein's original paper is available at \n\nhttp://projecteuclid.
 org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.bsms
 p/1200501656\n\n\n
LOCATION:MR12\, CMS
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