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February 2021 A class of asymmetric regression models for left-censored data
Helton Saulo, Jeremias Leão, Juvêncio Nobre, Narayanaswamy Balakrishnan
Braz. J. Probab. Stat. 35(1): 62-84 (February 2021). DOI: 10.1214/20-BJPS494


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.


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Helton Saulo. Jeremias Leão. Juvêncio Nobre. Narayanaswamy Balakrishnan. "A class of asymmetric regression models for left-censored data." Braz. J. Probab. Stat. 35 (1) 62 - 84, February 2021.


Received: 1 July 2019; Accepted: 1 October 2020; Published: February 2021
First available in Project Euclid: 6 January 2021

MathSciNet: MR4195760
Digital Object Identifier: 10.1214/20-BJPS494

Rights: Copyright © 2021 Brazilian Statistical Association


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Vol.35 • No. 1 • February 2021
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