Sequential shrinkage estimation of the difference between two multivariate normal means

Abstract

The paper considers sequential estimation of the difference of two -variate normal means from independent populations when the variance covariance matrix from each population is known up to a scalar multiple and are not necessarily equal. The sampling scheme is a multivariate extension of the stopping rule proposed by Ghosh and

Mukhopadhyay (1980). A class of James Stein estimators that dominates the difference of sample mean vectors is developed and asymptotic risk expansions are also provided.

Keywords:

• normal means
• independent populations
• bacrward martingale
• Behren s Fisher
• Sequential estimation
• James Stein estimators
• asymptotic risk expansion