Bias correction for a class of multivariate nonlinear regression models

In this paper, we derive general formulae for second-order biases of maximum likelihood estimates which can be applied to a wide class of multivariate nonlinear regression models. The class of models we consider is very rich and includes a number of commonly used models in econometrics and statistics as special cases, such as the univariate nonlinear model and the multivariate linear model. Our formulae are easy to compute and give bias-corrected maximum likelihood estimates to order n-1, where n is the sample size, by means of supplementary weighted linear regressions. They are also simple enough to be used algebraically in order to obtain closed-form expressions in special cases.