Sequential shrinkage estimation of linear regression parameters

Abstract

The paper considers estimation of p(>3) linear regression parameters (including the mean) under sequential sampling in a Gauss Markoff setup. A class of James Stein estimators that dominates the least squares estimator is developed, and an asymptotic risk expansion is given for both the least squares and James Stein estimators.

Keywords:

• sequential estimation
• James-stein estimators
• regression parameters
• Gauss Markoff setup
• asymptotic risk expansion
• submartingales
• least squares