A parametric quantile regression approach for modelling zero-or-one inflated double bounded data

Abstract

Over the last decades, the challenges in applied regression have been changing considerably, and full probabilistic modeling rather than predicting just means is crucial in many applications. Motivated by two applications where the response variable is observed on the unit-interval and inflated at zero or one, we propose a parametric quantile regression considering the unit-Weibull distribution. In particular, we are interested in quantifying the influence of covariates on the quantiles of the response variable. The maximum likelihood method is used for parameters estimation. Monte Carlo simulations reveal that the maximum likelihood estimators are nearly unbiased and consistent. Also, we define a residual analysis to assess the goodness of fit.

Keywords: parametric quantile regression; proportions; unit-Weibull distribution; zero-or-one inflated models.