A Note on the Comparison of the Stein Estimator and the James-Stein Estimator

Abstract

The seminal work of Stein (1956) showed that the maximum likelihood estimator (MLE) of the mean vector of a p-dimensional multivariate normal distribution is inadmissible under the squared error loss function when p ⩾ 3 and proposed the Stein estimator that dominates the MLE. Later, James and Stein (1961) proposed the James-Stein estimator for the same problem and received much more attention than the original Stein estimator. We re-examined the Stein estimator and conducted an analytic comparison with the James-Stein estimator. We found that the Stein estimator outperforms the James-Stein estimator under certain scenarios and derived the sufficient conditions.

Keywords:

• Stein estimator
• James-Stein estimator
• Mean squared error.

Mathematics Subject Classification:

• 62H12; 62F10.