Seminar Details

Seminar Details

Monday

Jan 9

3:30 pm

## The Role of Reversal in Statistics: Two Vignettes

### Michael Perlman

Seminar

University of Washington - Department of Statistics

1. Reversing Monotonicity in Order-restricted Inference Can be Good.
An order-restricted (OR) 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 (ORLRTs) and maximum likelihood estimators (ORMLEs) have been criticized on the grounds that they may violate a â€œcone-order monotonicityâ€ (COM) property relative to $C$; instead they may â€œreverseâ€ the cone-order. It is argued here, however, that these reversals occur only in the case that $C$ is an {\it obtuse} cone, and that in this case COM is an inappropriate requirement for OR tests and estimates. Therefore the ORLRT and ORMLE remain perfectly reasonable procedures for OR inference.

2. Reversing the Stein Effect Can be Bad.
The {\it 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. Instead, he/she will likely incur a greater error than if shrinkage were not used.

[Joint work with Sanjay Chaudhuri, National University of Singapore]

Background papers are available as Technical Report no. 434 and 491:

http://www.stat.washington.edu/www/research/reports/2003/tr434.pdf

http://www.stat.washington.edu/www/research/reports/2005/tr489.pdf