Geary on inference in multiple regression and on closeness and the Taxi problem

Abstract

This paper deals with some minor aspects of Roy Geary's work. Two areas are selected for discussion ? (a) his work with Leser on "paradoxical" situations in multiple regression and (b) his work on estimation of the unknown upper bound, N, of a uniform distribution, based on a sample of n values from that distribution. This work is explained, expanded and evaluated. The concept of "paradoxes" in multiple regression is slightly extended and applied to the case of estimating means in a multinomial situation with a known covariance matrix. Geary's estimator of N is compared with several other estimators, on the basis, inter alia, of mean squared errors, in both the cases of a continuous distribution and a discrete distribution sampling without replacement. In the latter case, a "large N minimum mean squared error" estimator is derived and assessed.