Open Access
Translator Disclaimer
December, 1985 Two-Stage Sequential Estimation of a Multivariate Normal Mean under Quadratic Loss
Jayalakshmi Natarajan, William E. Strawderman
Ann. Statist. 13(4): 1509-1522 (December, 1985). DOI: 10.1214/aos/1176349752


In estimating a multivariate normal mean under quadratic loss, this paper looks into the existence of two-stage sequential estimators that are better both in risk (mean square error) and sample size than the usual estimator of a given fixed sample size. In other words, given any sample size $n$, we are looking for two-stage sequential estimators truncated at $n$, with a positive probability of stopping earlier and risk lower than that of the sample mean based on $n$ observations. Sequential versions of James-Stein estimators are used to produce two-stage sequential estimators better in risk and sample size than the usual estimator--the sample mean. A lower bound on the largest possible probability of stopping earlier without losing in the risk is also obtained.


Download Citation

Jayalakshmi Natarajan. William E. Strawderman. "Two-Stage Sequential Estimation of a Multivariate Normal Mean under Quadratic Loss." Ann. Statist. 13 (4) 1509 - 1522, December, 1985.


Published: December, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0591.62072
MathSciNet: MR811508
Digital Object Identifier: 10.1214/aos/1176349752

Primary: 62F10
Secondary: 62C99, 62H12

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 4 • December, 1985
Back to Top