統計学輪講（第８回）

日時      2010年05月18日(火)    15時～16時40分
場所      経済学部新棟３階第３教室
講演者    William E. Strawderman (Rutgers University)
演題      Robust Bayes minimax estimators of location vectors

概要

We study estimation of the mean vector of a spherically symmetric distribution
with a residual vector. This is a version of the canonical form
of a general linear model with a spherically symmetric
(but not necessarily normal) error distribution.
Loss is the scaled sum of squared errors. A version of Stein's lemma
which holds for such distributions allows one to determine a subclass
of estimators
which are minimax (and beat the Least Squares estimator) simultaneously
for the entire class of spherically symmetric distributions.
Further Maruyama noticed that certain classes of prior distributions
lead to General Bayes estimators that are also independent
of the underlying spherically symmetric distribution.
Maruyama (03), Maruyama and Strawderman (05, 09),
and Fourdrinier and Strawderman (09) studied classes of estimators
that have the double robustness property of being simultaneously
Generalized Bayes and minimax for the entire class
of spherically symmetric error distributions.
This talk describes these results and some of the ongoing work in this area.
Much of the work is joint with Yuzo Maruyama and Dominique Fourdrinier.