A0485
Title: Confidence interval and hypothesis testing for high-dimensional quantile regression: Convolution smoothing and debiasing
Authors: Yibo Yan - East China Normal University (China) [presenting]
Abstract: L1-penalized quantile regression (L1-QR) is a useful tool for modeling the relationship between input and output variables when detecting heterogeneous effects in a high-dimensional setting. Hypothesis tests can then be formulated based on the debiased L1-QR estimator that reduces the bias induced by the Lasso penalty. However, the non-smoothness of the quantile loss brings great challenges to the computation, especially when the data dimension is high. Recently, the convolution-type smoothed quantile regression (SQR) model has been proposed to overcome such shortcomings, and people developed the theory of estimation and variable selection therein. The debiased method is combined with the SQR model and comes up with the debiased L1-SQR estimator, based on which confidence intervals and hypothesis testing are then established in the high-dimensional setup. Theoretically, the non-asymptotic Bahadur representation is provided for the proposed estimator and also the Berry-Esseen bound, which implies the empirical coverage rates for the studentized confidence intervals. Furthermore, the theory of hypothesis testing is built on both a single variable and a group of variables. Finally, extensive numerical experiments are exhibited on both simulated and real data to demonstrate the method's good performance.
