Model checking in Tobit regression via nonparametric smoothing

This paper proposes a class of lack-of-fit tests for checking the adequacy of a presumed parametric form of the regression function in Tobit regression models. This class of tests is a weighted adaptation of the Zheng’s test for fitting a parametric regression model. The asymptotic null distributions of the underlying test statistics are shown to be normal. Moreover, the consistency of these tests against some fixed alternatives and asymptotic power against some local nonparametric alternatives are also derived. An optimal test within the proposed class of tests against a given sequence of nonparametric local alternatives is identified. A finite sample simulation shows some superiority of some of the proposed tests, compared to some of the existing tests.