on the second-order bias of parameter estimates in nonlinear regression models with student t errors

Abstract

In this paper, we derive general formulae for second-order biases of maximum likelihood estimates of the regression, dispersion and precision parameters in nonlinear regression models with t distributed errors. Our formulae are easy to compute, giving the biases by means of ordinary linear regressions. They generalize some previous results due to Cook, Tsai and Wei (1986); Cordeiro and McCullagh (1991) and Cordeiro and Vasconcellos (1997). We derive simple closed-form expressions for these biases in special models. We present some simulations that indicate that the bias-corrected estimates produce a reduction in bias without a given corresponding increase in variability. The bias correction achieves a second-order reduction in the mean square errors of the corrected estimates.

Keywords:

• Bias correction
• Cauchy model
• maximum likelihood estimate
• nonlinear regression model
• tdistribution