Comparison of Point Estimators of Normal Percentiles
Dyer, Danny D.
Hensley, Onas L.
Keating, Jerome P.
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There are available several point estimators of the percentiles of a normal distribution with both mean and variance unknown. Consequently, it would seam appropriate to make a comparison among the estimators through sums "closeness to the true value" criteria. Along these lines, the concept of Pitman-closeness efficiency is introduced. Essentially, when comparing two estimators, the Pitman-closeness efficiency gives "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 unbissed 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.