More About Geary and the Taxi Problem

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 discussions of Geary's estimator and alternatives is used to explain the problem and suggest solutions.