Model diagnostics of parametric Tobit model based on cumulative residuals

Abstract

In this paper, we investigate the adequate check of the parametric Tobit model. A Cramer–Von Mises type test statistic is constructed, and its asymptotic properties under the null and alternative hypotheses are rigorously studied. The method is effective for the adequacy check of parametric regression models with a scalar or multivariate covariate. Furthermore, it avoids the nonparametric smoothing of the regression function and the choice of the smoothing parameter. Simulation studies are conducted to compare the performance of the proposed test procedure and the existing methods in the literature. A real data set of income is analyzed by applying the proposed method.