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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big STATISTICS SEMINAR}
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\centerline{4:15 p.m., Tuesday, May 11, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in the 1st Floor Lounge)}


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\centerline{\sl Brad Efron}
\centerline{\sl Stanford University}
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\centerline{\bf Confidence Regions and Inferences for a Multivariate Normal Mean Vector}
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Abstract:

We wish to form a confidence region for mu having observed x~N(mu,I),
x and mu both n-dimensional vectors. The standard region is a sphere
centered at x, with radius determined by the chisquared distribution. A
succession of authors, beginning with Charles Stein, have proposed
regions having smaller volume than the standard. I will review these
proposals and present a general approach for such constructions. It
isn't clear that smaller volume leads to improved inferential
properties, as demonstrated by an example.


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