Distribution-free test in Tobit mean regression model

This paper discusses the problem of fitting a parametric model in Tobit mean regression models. The proposed test is based on the supremum of the Khamaladze-type transformation of a partial sum process of calibrated residuals. The asymptotic null distribution of this transformed process is shown to be the same as that of a time-transformed standard Brownian motion. Consistency of this sequence of tests against some fixed alternatives and asymptotic power under some local nonparametric alternatives are also discussed. Simulation studies are conducted to assess the finite sample performance of the proposed test. The power comparison with some existing tests shows some superiority of the proposed test at the chosen alternatives.