A class of asymmetric regression models for left-censored data

A common assumption regarding the standard tobit model is the normality of the error distribution. However, asymmetry and bimodality may be present and alternative tobit models must be used. In this paper, we propose a tobit model based on the class of log-symmetric distributions, which includes as special cases heavy and light tailed distributions and bimodal distributions. We implement a likelihood-based approach for parameter estimation and derive a type of residual. We then discuss the problem of performing testing inference in the proposed class by using the likelihood ratio and gradient statistics, which are particularly convenient for tobit models, as they do not require the information matrix. A thorough Monte Carlo study is presented to evaluate the performance of the maximum likelihood estimators and the likelihood ratio and gradient tests. Finally, we illustrate the proposed methodology by using a real-world data set.