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SUMMARY:Optimal Shrinkage Estimation in Heteroscedastic Hierarchical Model
 s - Samuel Kou\, Harvard University
DTSTART:20111202T160000Z
DTEND:20111202T170000Z
UID:TALK33355@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:Hierarchical models are powerful statistical tools widely used
  in scientific\nand engineering applications. The homoscedastic (equal var
 iance) case has\nbeen extensively studied\, and it is well known that shri
 nkage estimates\,\nthe James-Stein estimate in particular\, offer nice the
 oretical (e.g.\, risk)\nproperties. The heteroscedastic (the unequal varia
 nce) case\, on the other\nhand\, has received less attention\, even though
  it frequently appears in real\napplications. It is not clear of how to co
 nstruct "optimal" shrinkage\nestimate. In this talk\, we study this proble
 m. We introduce a class of\nshrinkage estimates\, inspired by Stein's unbi
 ased risk estimate. We will\nshow that this class is asymptotically optima
 l in the heteroscedastic\ncase. We apply the estimates to real examples an
 d observe excellent\nnumerical results.\n\nThis talk is based on joint wor
 k with Lawrence Brown and Xianchao Xie.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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