A further look at the comparison of normal percentile estimators

Abstract

For the purpose of making a pairwise comparison of point estimators of normal percentiles, a twofold technique is introduced which basically examines (a) the"odds"in favor of an estimator being closer to the true value than is a competing estimator and (b) an estimator's average closeness to the true value when it is closer (as well as when it is not) than is a competing estimator, Closeness to the true value is measured through an absolute error loss function. Joint consideration of these concepts is shown to form a basis for determining which of two estimators is preferred in a given situation.

Keywords:

• pitman-closeness efficiency
• conditional mean absolute error
• maximum likelihood
• minimum variance
• unbiased
• best invariant
• median unbiased
• minimum mean absolute error