Improved transformation-based quantile regression

Modelling the quantiles of a random variable is facilitated by their equivariance to monotone transformations. In conditional modelling, transforming the response variable serves to approximate nonlinear relationships by means of flexible and parsimonious models; these usually include standard transformations as special cases. Transforming back to obtain predictions on the original scale or to calculate marginal nonlinear effects becomes a trivial task. This approach is particularly useful when the support of the response variable is bounded. We propose novel transformation models for singly or doubly bounded responses, which improve upon the performance of conditional quantile estimators as compared to other competing transformations, namely the Box–Cox and the Aranda-Ordaz transformations. The key is to provide flexible transformations with range the whole of the real line. Estimation is carried out by means of a two-stage estimator, while confidence intervals are obtained by bootstrap. A simulation study and some illustrative data analyses are presented