Sufficient dimension reduction for conditional quantiles with alternative types of data

There is a great amount of work that stands to benefit from quantile regression (QR), especially when the extreme parts of data are of interest. Although QR has been well developed, it has recently received particular interest in the area of dimension reduction. Existing dimension reduction techniques for conditional quantiles focus on commonly used types of data, such as quantitative predictor variables without any time-dependent structure. However, in this work we show how partial dimension reduction techniques can be extended to conditional quantiles in order to facilitate analysing data involving both quantitative and categorical predictor variables and/or longitudinal data. Simulation examples and a real data application demonstrate the easy to implement algorithm and its good finite sample performance.