A common assumption in the standard tobit model is the normality for the error distribution. However, asymmetry and bimodality may be present and alternative tobit models must be used in such cases. In this paper, we propose a tobit model based on the class of log-symmetric distributions, which includes as special cases heavy/light tailed distributions and bimodal distributions. We implement a likelihood-based approach for parameter estimation and consider a type of residual. We then discuss the problem of performing hypothesis tests within 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. An elaborate Monte Carlo study is carried out for evaluating the performance of the maximum likelihood estimates, the likelihood ratio and gradient tests and the empirical distribution of the residuals. Finally, we illustrate the proposed methodology with the use of a real data set.
"A class of asymmetric regression models for left-censored data." Braz. J. Probab. Stat. 35 (1) 62 - 84, February 2021. https://doi.org/10.1214/20-BJPS494