Nonlinear dimension reduction for conditional quantiles

In practice, data often display heteroscedasticity, making quantile regression (QR) a more appropriate methodology. Modeling the data, while maintaining flexible nonparametric fitting, requires smoothing over high-dimensional space which might not be feasible when number of predictor variables is large. This problem makes necessary use dimension reduction techniques for conditional quantiles, focus on extracting linear combinations without losing any information about quantile. However, nonlinear features can achieve greater reduction. We, therefore, present first extension algorithm estimating central subspace (CQS) using kernel data. First, we describe feature CQS within framework reproducing Hilbert space, and second, illustrate its performance through simulation examples real applications. Specifically, emphasize visualizing various aspects structure two extractors, highlight ability to combine proposed with classification algorithms. The results show that an effective tool performing quantiles.