Transformed central quantile subspace

Quantile regression (QR) is a well-established method of tail analysis. Application of QR can become very challenging when dealing with high-dimensional data, thus requiring dimension reduction techniques. While the current literature on these techniques focuses on extracting linear combinations of the predictor variables that contain all the information about the conditional quantile, non-linear features can potentially achieve greater dimension reduction. We, therefore, present the first application of transformed dimension reduction for conditional quantiles, which serves as an intermediate step between linear and nonlinear dimension reduction. The idea is to transform the predictors monotonically and then look for low-dimensional projections by applying linear dimension reduction techniques. The performance of the proposed methodology is demonstrated through simulation examples and a real data application.