A simple nonparametric test for diagnosing nonlinearity in Tobit median regression model

In many applications, the response variable is observed only when it is above or below a given threshold otherwise the threshold itself is observed. Tobit median regression model is a useful semiparametric procedure for analyzing this type of censored data. We propose a simple nonparametric test for assessing the common linearity assumption in this model. Compared to those existing methods in the literature, the new test has the advantage of allowing the alternative to be any smooth function. In addition, it does not require any knowledge of the parametric distribution of the random error. The test is asymptotically normal under the null hypothesis of linearity. A small Monte Carlo study demonstrates its performance.