Model checking in Tobit regression with measurement errors using validation data

- In Tobit EIV models, a class of nonparametric lack-of-fit tests are proposed.
- The proposed tests are shown to be robust to the choices of parameter estimators.
- A bandwidth selection strategy is proposed and it shows good simulation results.

This article proposes a class of lack-of-fit tests for fitting a parametric regression function in Tobit regression models with measurement error in covariates when validation data is available. The empirical residuals based on nonparametric regression function estimators are used to construct an analog of the Zheng's class of test statistics. The proposed class of tests is robust to the choices of parameter estimators and consistent against a large class of fixed alternatives. We also establish the asymptotic normality of these test statistics under the null hypothesis and under a sequence of local alternatives. A finite sample simulation study shows some superiority of a member of the proposed class of tests over the two existing tests in terms of empirical power.