The Pitman Closeness of a Class of Scaled Estimators

Scaling is known to reduce the mean square error of unbiased estimators of the mean. Pitman closeness, like mean square error, is often used as a criterion for comparing competing estimators. Scaling is reexamined from the perspective of Pitman closeness. Scaling is found to offer not only reduced mean square error, but also, in many cases, an advantage in terms of Pitman closeness. However, these advantages accrue to a substantial degree only in experiments with low signal-to-noise ratio and very costly measurements.