Discrimination between quantile regression models for bounded data

Abstract

Most often when we use the term `bounded', we mean a response variable that retains inherent upper and lower boundaries; for instance, it is a proportion or a strictly positive for example incomes. This constraint has implications for the type of model to be used since most traditional linear models may not respect these boundaries. Parametric quantile regression with bounded data thus comes with a framework for analysis and interpretation of how the predictor of interest influences the response variable over different quantiles while constrained by the bounds of the theoretically assumed distribution. In this paper, several parametric quantile regression models are explored and their performance is investigated under several conditions. Our Monte Carlo simulation results suggest that some of these parametric quantile regression models can bring significant improvement relative to other existing models under certain conditions.