Generalized Asymptotic Regression and Non-Linear Path Analysis

Abstract

Statistical models which approach an asymptote are classified into two categories: (1) rational models, and (2) transcendental models. The first is given a general statistical treatment. A special class of transcendental model, termed the "single process" law, is studied both in terms of its elementary geometrical properties and in terms of finding statistical estimation and testing procedures for it. The maximum likelihood estimation procedure is outlined and a new "parabolic" test is described which may be used for finding a confidence region for the non-linear parameters, even for small samples. The ideas of linear path analysis, wherein several variables are related in a cause and effect scheme, is extended to include the single process law. Certain parallels between the linear and non-linear case are established and a general estimation scheme for the non-linear scheme is described.