[Colloquium] [statseminars] REMINDER TODAY - Statistics Seminar: MICHAEL PERLMAN, Univ Washington, Eckhart 133 at 4pm

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The University of Chicago
Department of Statistics
Seminar Series

MICHAEL PERLMAN
Department of Statistics
University of Washington

The Role of Reversals in Statistical inference: Two Vignettes

MONDAY, May 12, 2008 at 4:00 PM
133 Eckhart Hall, 5734 S. University Avenue
Refreshments following the seminar in Eckhart 110.

ABSTRACT

I. Reversing Monotonicity in Order-restricted Inference.

An order-restricted statistical model can be viewed as one whose 
parameter space is a closed convex cone C in a Euclidean space. 
Order-restricted likelihood ratio tests and maximum likelihood 
estimators have been criticised on the grounds that they may violate a 
"cone-order monotonicity" (COM) property relative to C; instead they may 
“reverse” the cone-order. It is argued here, however, that these 
reversals occur only in the case that C is an obtuse cone, and that in 
this case COM is an inappropriate requirement for order-restricted tests 
and estimates. The likelihood ratio test and maximum likelihood 
estimator remain perfectly reasonable procedures for order-restricted 
inference.

2. Reversing the Stein Effect.

The Reverse Stein Effect is identified and illustrated: A statistician 
who shrinks his/her parameter estimate toward a point based on the 
observed data rather than on reliable prior information will not be 
protected by the minimax property of shrinkage estimators such as
that of James and Stein. The curvature of high-dimensional space that 
produces the classical Stein Effect works here almost exactly in reverse 
- a shrinkage estimator will likely incur a much greater error than the 
ordinary (best invariant) estimator.

[Joint work with Sanjay Chaudhuri, National University of Singapore]
Please send email to Mathias Drton (drton at galton.uchicago.edu
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