THE PITMAN CLOSENESS OF A CLASS OF SCALED ESTIMATORS

Scaling is known to reduce the mean square error of unbiased estimator s of the mean. Pitman closeness, like mean square error, is often used as a criterion for comparing competing estimators. Scaling is reexami ned from the perspective of Pitman closeness. Scaling is found to offe r not only reduced mean square error, but also, in many cases, an adva ntage in terms of Pitman closeness. However, these advantages accrue t o a substantial degree only in experiments with low signal-to-noise ra tio and very costly measurements.