Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1150754 | Journal of Statistical Planning and Inference | 2006 | 18 Pages |
Abstract
This paper deals with the empirical Bayes testing for the mean θ of a N(θ,Ï2) distribution using a linear error loss where it is assumed that θ follows an unknown prior distribution G and variance Ï2 is fixed but unknown. An empirical Bayes test δËn is constructed. Under very mild conditions that EG[|θ|]<â and the critical point of a Bayes test is finite, δËn is shown to be asymptotically optimal, and the associated regret converges to zero at a rate O(n-1(lnn)1.5)where n is the number of past experiences available when the current component decision problem is considered. This rate achieves the optimal rate which was established by Gupta and Li (Optimal rate of convergence of monotone empirical Bayes tests for a normal mean. Technical Report 01-03, Department of Statistics, Purdue University.) for variance Ï2 known case.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
TaChen Liang,