Bias corrected estimates in multivariate student t regression models

Abstract

The t distribution has proved to be a useful alternative to the normal distribution especially When robust estimation is desired. We consider the multivariate nonlinear Student-t regression model and show that the biased of the estimates of the regression coefficients can be computed from an auxiliary generalized linear regression. We give a formula for the biases of the estimates of the parameters in the scale matrix, which also can be computed by means of a generalized linear regression. We briefly discuss some important special cases and present simulation results which indicate that our bias-corrected estimates outperform the uncorrected ones in small samples.

Keywords:

• Bias correction
• log-likelihood derivatives
• maximum likelihood estimation
• multivariate nonlinear regression
• multivariate Student-t distribution.