Partially Adaptive Estimation of Regression Models via the Generalized T Distribution

This paper considers M-estimators of regression parameters that make use of a generalized functional form for the disturbance distribution. The family of distributions considered is the generalized t (GT), which includes the power exponential or Box-Tiao, normal, Laplace, and t distributions as special cases. The corresponding influence function is bounded and redescending for finite “degrees of freedom.” The regression estimators considered are those that maximize the GT quasi-likelihood, as well as one-step versions. Estimators of the parameters of the GT distribution and the effect of such estimates on the asymptotic efficiency of the regression estimates are discussed. We give a minimum-distance interpretation of the choice of GT parameter estimate that minimizes the asymptotic variance of the regression parameters.