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Title: Penalized kernel quantile regression for varying coefficient models Authors:  Eun Ryung Lee - Sungkyunkwan University (Korea, South) [presenting]
Abstract: Kernel smoothing has been a prevalent and successful nonparametric estimation method in the literature. Nevertheless, a penalization technique in kernel smoothing has been poorly understood due to its intrinsic technical and computational issues. We develop a novel penalized and computational method working with local linear quantile regression in varying coefficient models. We show that the proposed method consistently identifies the partially linear structure of the varying coefficient model even when the number of covariates is allowed to increase with the sample size. We develop an efficient algorithm using the alternating direction method of multipliers with a computational convergence guarantee. Such development requires novel technical and computational analyses, especially when the dimension diverges to infinity. The proposed method outperforms the existing penalized kernel algorithms, and it can be easily extended to other problems in penalized kernel smoothing. The various simulations and real data analyses conducted illustrate the effectiveness and numerically verify the proposed method.