Abstract
This paper derives the asymptotic expansions of the distribution function of the maximum likelihood estimator (MLE) and the log likelihood ratio (LR) test in a nonlinear regression model. It reports on an investigation of the effects of nonlinearity of a model on the asymptotic expansions by making use of two kinds of curvature measures: intrinsic curvature and parameter effect curvature defined by Bates and Watts (1980). It shows, after suitable transformation, that the distribution function of the MLE up to O(T-1/2) is related to only the parameter effect curvature. The intrinsic curvature appears only in a term of O(T-1) in the distribution of LR. Furthermore, this paper illustrates that the intrinsic curvature is essentially equivalent to Efron's statistical curvature.
