A Note on Alternative Matrix Entry Estimation Techniques

Estimation of trip tables and other matrices that are subject to constraints is a common practical problem. This note reviews four common estimation methods: (1) minimization of the sum of absolute deviations, (2) the biproportional technique, (3) information minimization and (4) constrained generalized least squares (CGLS) regression. A small example illustrates their application. Computational approaches and burdens as well as implicit error structure assumptions are reviewed. The paper concludes that estimates obtained from the biproportional, information minimization and CGLS regression (with a chi-square type error distribution assumption), are likely to be similar in practice. Choice of an appropriate technique depends upon a priori assumptions of error structures, relative computational burdens and the usefulness of estimate uncertainty measures.