William E. Strawderman, Rutgers University

Improved Estimation of Location Parameters

We consider simultaneous estimation of the parameters of a multivariate location family. About half the talk will be devoted to an intuitive discussion of certain types of so-called shrinkage estimators. The discussion will focus on; (1) What type of estimators might be expected to perform better than the classical least squares estimators, (2) When can large improvements be expected, and (3) How large an improvement can be expected. The aim will be to indicate that the phenomenon of improvement over classical procedures via shrinkage is not particularly dependent on the assumption of an underlying normal distribution. We give some theoretical results which give support to this thesis.