Bias-Corrected Maximum Likelihood Estimators in Nonlinear Heteroscedastic Models

Abstract

Nonlinear heteroscedastic models are widely used in econometrics and statistical applications. We derive matrix formulae for the second-order biases of the maximum likelihood estimators of the parameters in the mean and variance response which generalize previous results by Cook et al. (1986) and Cordeiro (1993). The biases of the estimators are easily obtained as vectors of regression coefficients from suitable weighted linear regressions. The practical use of such biases is illustrated in a simulation study and in an application to a real data set.

Keywords:

• Bias correction
• Cumulant
• Heteroscedastic model
• Information matrix
• Maximum likelihood
• Method of scoring
• Nonlinear model

Mathematics Subject Classification:

• 62J02
• 62F10
• 62F12

Acknowledgment

We are very grateful to two referees for helpful comments that considerably improved the article. We gratefully acknowledge financial support from CNPq and FACEPE.