This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.
Abstract Details
Activity Number:
|
519
|
Type:
|
Contributed
|
Date/Time:
|
Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
|
Sponsor:
|
IMS
|
Abstract - #308336 |
Title:
|
Optimal Estimation of Multidimensional Normal Means with Unknown Variances
|
Author(s):
|
Xu Han*+ and Lawrence D. Brown
|
Companies:
|
Princeton University and University of Pennsylvania
|
Address:
|
Room 216, Sherrerd Hall, Princeton, NJ, 08544, USA
|
Keywords:
|
normal mean problem ;
admissibility ;
generalized Bayes estimator ;
unknown variance ;
shrinkage estimator ;
minimaxity
|
Abstract:
|
Let $X\sim N_p(\theta,\sigma^2I)$ and $W\sim\sigma^2\chi_m^2$, where both $\theta$ and $\sigma^2$ are unknown. We consider estimation of $\theta$ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for $\theta$ are admissible. This paper has a two-fold purpose: 1. Provide a benchmark for the evaluation of shrinkage estimation for a multivariate normal mean with unknown variance; 2. Use admissibility as a criterion to select priors for hierarchical Bayes models. To illustrate how to select hierarchical priors, we apply these sufficient conditions to a widely used hierarchical Bayes model proposed by Maruyama \& Strawderman (2005), and obtain a class of admissible and minimax generalized Bayes estimators for the normal mean $\theta$.
|
The address information is for the authors that have a + after their name.
Authors who are presenting talks have a * after their name.
Back to the full JSM 2010 program
|
2010 JSM Online Program Home
For information, contact jsm@amstat.org or phone (888) 231-3473.
If you have questions about the Continuing Education program, please contact the Education Department.