Quasi-Cauchy Regression Modeling for Fractiles Based on Data Supported in the Unit Interval

Abstract

A fractile is a location on a probability density function with the associated surface being a proportion of such a density function. The present study introduces a novel methodological approach to modeling data within the continuous unit interval using fractile or quantile regression. This approach has a unique advantage as it allows for a direct interpretation of the response variable in relation to the explanatory variables. The new approach provides robustness against outliers and permits heteroscedasticity to be modeled, making it a tool for analyzing datasets with diverse characteristics. Importantly, our approach does not require assumptions about the distribution of the response variable, offering increased flexibility and applicability across a variety of scenarios. Furthermore, the approach addresses and mitigates criticisms and limitations inherent to existing methodologies, thereby giving an improved framework for data modeling in the unit interval. We validate the effectiveness of the introduced approach with two empirical applications, which highlight its practical utility and superior performance in real-world data settings.