Elliptical regression models for multivariate sample-selection bias correction

In linear regression, a multivariate sample-selection scheme often applies to the dependent variable, which results in missing observations on the variable. This induces the sample-selection bias, i.e. a standard regression analysis using only the selected cases leads to biased results. To solve the bias problem, in this paper, we propose a class of multivariate selection regression models by extending classic Heckman model to allow for multivariate sample-selection scheme and robustness against departures from normality. Necessary theories for building a formal bias correction procedure, based upon the proposed model, are obtained, and an efficient estimation method for the model is provided. Simulation results and a real data example are presented to demonstrate the performance of the estimation method and practical usefulness of the multivariate sample-selection models.