Comparing Estimators for Population Variance Using Pitman Nearness

Abstract

As a classroom example, some researchers considered the problem of estimation of the variance of a normal population with known mean. They showed that the maximum likelihood estimator under the unknown mean assumption has smaller mean squared error than that under the known mean assumption, thereby implying that one would be “better off” by ignoring the information provided by the known mean. This same problem is reconsidered under the Pitman nearness criterion.

Key Words:

• Mean squared error
• Median