Quantiles for Fractions and Other Mixed Data

This paper studies the estimation of quantile regression for fractional data, focusing on the case where there are mass-points at zero or/and one. More generally, we propose a simple strategy for the estimation of the conditional quantiles of data from mixed distributions, which combines standard results on the estimation of censored and Box-Cox quantile regressions. The implementation of the proposed method is illustrated using a well-known dataset.