Empirical minimum distance lack-of-fit tests for Tobit regression models

Abstract

The purpose of this report is to propose and evaluate two lack-of-fit test procedures to check the adequacy of the regression functional forms in the standard Tobit regression models. It is shown that testing the null hypothesis for the standard Tobit regression models amounts testing a new equivalent null hypothesis of the classic regression models. Both procedures are constructed based on the empirical variants of a minimum distance, which measures the squared difference between a nonparametric estimator and a parametric estimator of the regression functions fitted under the null hypothesis for the new regression models. The asymptotic null distributions of the test statistics are investigated, as well as the power for some fixed alternatives and some local hypotheses. Simulation studies are conducted to assess the finite sample power performance and the robustness of the tests. Comparisons between these two test procedures are also made.