A Simple Method for Fitting an Asymptotic Regression Curve

Abstract

Simple methods for fitting the asymptotic regression equation y = [alpha] - [beta] [rho] x are suggested for 4, 5,6 or 7 equally spaced values of x. The estimates of p are given by n-1 n-1 r = ria^y./r^..a.y. 1 where the a. are 4, 1, -5 for 4 values of x, 4, 3,-1, -6, for 5 values, 4, 4, 2, -3, -7, for 6 values, and 1, 1, 1, -1, -2, for 7 values. The efficiencies of these estimates of [rho] , relative to maximum likelihood estimates, are high over the useful range of values of [rho]. Estimates of a and B are given by the regressions of y on rx.