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CATEGORIES:Statistics Reading Group
SUMMARY:Charles Stein's 1956 inadmissibility paper - Larry
Brown\, Statistics Department\, University of Pen
nsylvania
DTSTART;TZID=Europe/London:20081016T170000
DTEND;TZID=Europe/London:20081016T180000
UID:TALK14652AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14652
DESCRIPTION:Just over 50 years ago Stein published a startling
statistical result. (Stein (1956).) When three or
more normal means are to be estimated the sample
mean is not an admissible estimator. It is better
to 'shrink' towards the origin\, or some other pre
determined point. At first this fact appeared to
many as a mathematical peculiarity\, with no parti
cular practical significance. Publication five yea
rs later of the James-Stein (1961) estimator demon
strated that the difference in performance could b
e quite substantial between the sample mean and a
suitable shrinkage estimator. It\nhas become under
stood in the intervening decades how this minimax
surprise is intimately related to a variety of oth
er practical statistical methodologies and its pri
nciples applicable in a wide range of practical\ns
ettings.\n \nStein's original paper include
d a geometrical explanation as to why such a parad
oxical result is inevitable when estimating suffic
iently many separate means\, as well a relatively
simple proof that 3 is sufficiently many. I'll sup
plement his geometric argument with a simple geome
tric diagram and then sketch his proof. I can also
remark about several generalizations (Brown (1966
)) of this proof that show this abnormal result is
not only a result about the normal distribution a
nd squared error loss (as some statisticians at th
e time had suspected).\n \nI don't specific
ally plan on discussing any further technicalities
\, but if time permits I can sketch where this sem
inal paper has led\, including especially James-St
ein (1961)\, mentioned above\, and Brown (1971)\nw
hich attempts to show that there are several relat
ed mathematical situations where 3>>2.\n \n[Inc
identally\, my Kuwait Lecture on Tuesday provides
a specific illustration of how shrinkage ideas can
be used in high dimensional data settings.]\n\nSt
ein's original paper is available at \n\nhttp://pr
ojecteuclid.org/DPubS/Repository/1.0/Disseminate?v
iew=body&id=pdf_1&handle=euclid.bsmsp/1200501656\n
\n\n
LOCATION:MR12\, CMS
CONTACT:Richard Samworth
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