In this paper, we investigate the adequate check of the parametric Tobit model. A Cramér–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.

在本文中，我们研究了参数Tobit模型的适当检查。构造了Cramér-VonMises类型检验统计量，并严格研究了其在原假设和替代假设下的渐近性质。该方法对于带有标量或多元协变量的参数回归模型的充分性检查有效。此外，它避免了回归函数的非参数平滑和平滑参数的选择。进行仿真研究以比较建议的测试程序和文献中现有方法的性能。通过应用所提出的方法来分析收入的真实数据集。