Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models

In this paper we derive general formulae for second-order biases of maximum-likelihood estimates in a class of symmetric nonlinear regression models. This class of models is commonly used for the analysis of data containing extreme or outlying observations in samples from a supposedly normal distribution. The formulae of the biases can be computed by means of an ordinary linear regression. They generalize some previous results by Cook et al., Biometrika 73 (1986) 615-623, Cordeiro and Vasconcellos, Statist. Probab. Lett. 35 (1997) 155-164 and Cordeiro et al., J. Statist. Comput. Simulation 60 (1998) 363-378. We derive simple closed-form expressions for these biases in special models. Simulation results are presented assessing the performance of the bias corrected estimates which indicate that they have smaller biases than the corresponding unadjusted estimates.