Maximum likelihood estimation of multivariate non-linear functional relationships

Abstract

The results of Dolby (1972) and Dolby and Feeeman (1975) on the estimation of an explicit non-linear functional relationship are examined for the multivariate case with Σknown up to a multiplicative constant. It is shown that in both univariate and multivariate situations the method of scoring for parameters is susceptible to major errors whenever the non-linearity implies asymmetric peaks or valleys and the data is relatively ”noisy”. Amendments to this method are proposed and demonstrated.