Improved transformation-based quantile regression

Modelling the quantiles of a random variable is facilitated by their equivariance to monotone trans-formations. In conditional modelling, transforming the response variable serves to approximate nonlinearrelationships by means of flexible and parsimonious models; these usually include standard transformationsas special cases. Transforming back to obtain predictions on the original scale or to calculate marginal non-linear effects becomes a trivial task. This approach is particularly useful when the support of the responsevariable 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 competingtransformations, namely the Box–Cox and the Aranda-Ordaz transformations. The key is to provide flexibletransformations with range the whole of the real line. Estimation is carried out by means of a two-stageestimator, while confidence intervals are obtained by bootstrap. A simulation study and some illustrativedata analyses are presented.The Canadian Journal of Statistics43: 118–132; 2015©2015 StatisticalSociety of Canada