Log-symmetric quantile regression models

TL;DR

This paper introduces a new class of quantile regression models based on reparameterized log-symmetric distributions, useful for modeling positive, asymmetric data, with validation through simulations and real data analysis.

Contribution

It proposes a novel quantile regression framework using log-symmetric distributions with a quantile parameter, expanding modeling options for positive asymmetric data.

Findings

Maximum likelihood estimators perform well in simulations.

Information criteria effectively select models.

The approach successfully analyzes real-world box office data.

Abstract

Regression models based on the log-symmetric family of distributions are particularly useful when the response is strictly positive and asymmetric. In this paper, we propose a class of quantile regression models based on reparameterized log-symmetric distributions, which have a quantile parameter. Two Monte Carlo simulation studies are carried out using the R software. The first one analyzes the performance of the maximum likelihood estimators, the information criteria AIC, BIC and AICc, and the generalized Cox-Snell and random quantile residuals. The second one evaluates the performance of the size and power of the Wald, likelihood ratio, score and gradient tests. A real box office data set is finally analyzed to illustrate the proposed approach.