Comparison of point estimators of normal percentiles

There are available several point estimators of the percentiles of a normal distribution with both mean and variance unknown. Consequently, it would seem appropriate to make a comparison among the estimators through some “closeness to the true value” criteria. Along these lines, the concept of Pitman-closeness efficiency is introduced. Essentially, when comparing two estimators, the Pit-man-closeness efficiency gives the “odds” in favor of one of the estimators being closer to the true value than is the other in a given situation. Through the use of Pitman-closeness efficiency, this paper compares (a) the maximum likelihood estimator, (b) the minimum variance unbiased estimator, (c) the best invariant estimator, and (d) the median unbiased estimator within a class of estimators which includes (a), (b), and (c). Mean squared efficiency is also discussed.