Log-symmetric quantile regression models

Regression models based on the log-symmetric family of distributions are particularly useful when the response variable is continuous, positive, and asymmetrically distributed. In this article, we propose and derive a class of models based on a new approach to quantile regression using log-symmetric distributions parameterized by means of their quantiles. Two Monte Carlo simulation studies are conducted utilizing the R software. The first one analyzes the performance of the maximum likelihood estimators, the Akaike, Bayesian, and corrected Akaike information criteria, and the generalized Cox–Snell and random quantile residuals. The second one evaluates the size and power of the Wald, likelihood ratio, score, and gradient tests. A web-scraped box-office data set of the movie industry is analyzed to illustrate the proposed approach. Within the main results of the simulation carried out, the good performance of the maximum likelihood estimators is reported.