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Title: Dimension reduction techniques for conditional quantiles Authors:  Eliana Christou - University of North Carolina at Charlotte (United States) [presenting]
Abstract: Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work on linear and nonlinear QR models. Specifically, nonparametric estimation of the conditional quantiles received particular attention, due to its model flexibility. However, nonparametric QR techniques are limited in the number of covariates. Dimension reduction offers a solution to this problem by considering low-dimensional smoothing without specifying any parametric or nonparametric regression relation. The existing dimension reduction techniques focus on the entire conditional distribution. We, on the other hand, turn our attention to dimension reduction techniques for conditional quantiles and introduce a new method for reducing the dimension of the predictor $X$. We propose both linear and nonlinear dimension reduction techniques for conditional quantiles, extend to alternative types of data (such as categorical and longitudinal predictors), and also consider functional predictors.