More about Geary and the "Taxi" problem

Abstract

Geary's treatment of the "taxi" problem was recently re-examined by Spencer and Largey (1993). This paper investigates the topic further, partly to place Geary's estimator in the context of more general methods and also because non-regular estimation situations are still of considerable theoretical interest. It is shown that Geary's estimator can be considered a case of an approach that equates a sufficient estimator to the median of its own distribution or of a modern method called the "Maximum Product of Spacings". Another approach of equating a sufficient estimator to its own expectation is considered and compared. Much of the interest in estimators for non-regular situations stems from the deficiencies of the maximum likelihood method in these cases. The discussion of Geary's estimator and alternatives is used to explain the problem and suggest solutions.