Spring Seminar Series April 24, 2008
University of Minnesota
School of Statistics
College
Absolute Penalty Estimation Versus Shrinkage Estimation
S. Ejaz
Ahmed
University of Michigan
and
University of Windsor
Thursday, April 24, 2008
3:30 PM, 115 Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford
Hall
Abstract
In this talk, I
consider a partially linear model where the vector of coefficients 
in the linear part can be
partitioned as (
) where 
is the
coefficient vector for main effects (e.g. treatment effect, genetic effects)
and is a
vector for ‘nuisance’ effects (e.g., age, lab). In this situation, inference about may benefit from moving the least squares estimate for
the full model in the direction of the least squares estimate without the
nuisance variables (Steinian shrinkage), or to drop
the nuisance variables if there is evidence that they do not provide useful
information (pre-testing). We
appraise the large-sample properties of shrinkage and pretest semi-parametric
estimators under quadratic loss and show that under general conditions a
shrinkage semi-parametric estimator improves on the full model conventional
semi-parametric least square estimator. We also consider an absolute penalty
estimation-type estimator (APE) and give a
Joint work with:
K. Doksum, S. Hossain and
J. You