Pitman Nearness Research Articles

A Short Note on Pitman's Measure of Nearness

Abstract Comparison of two estimators for a parameter θ is considered from the Pitman nearness (PN) point of view. An equivalence between PN and minimum mean squared error and minimum mean absolute error is achieved under some condition on the moments of a random variable.

A note on estimation of percentiles and reliability in the extreme-value distribution

A method for deriving point estimates of percentiles in the extreme-value distribution conditioned on the ancillary information is given. The resulting conditional median unbiased estimate is the same regardless of the arbitrary choice of equivariant estimators. The conditional median unbiased estimator is also shown to be optimal with respect to Pitman Nearness.