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Activity Number: 553
Type: Contributed
Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #321366 View Presentation
Title: Estimation and Variable Selection for the Quantile Partially Linear Single-Index Model
Author(s): Yuankun Zhang* and Heng Lian and Yan Yu
Companies: University of Cincinnati and University of New South Wales and University of Cincinnati
Keywords: Quantile regression ; Single-index models ; B-splines ; Check loss minimization ; SCAD ; Asymptotic normality

Partially linear single-index models are flexible dimension-reduction semiparametric tools yet still retain ease-of-interpretability as linear models. This paper is concerned with the estimation and variable selection for partially linear single-index quantile regression models. Polynomials splines are used to estimate the unknown link function. We first establish the asymptotic properties of the quantile regression estimators. For model selection, we adopt the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously selecting single-index variables as well as partially linear variables. We show that the regularized variable selection estimators are consistent and possess the oracle properties. The consistency and oracle properties are also established under the proposed linear approximation of the nonparametric link function that facilitates fast computation. Furthermore, we show that the proposed SCAD tuning parameter selectors via the Schwartz information criterion can consistently identify the true model. Monte Carlo studies as well as an application to Boston Housing data are presented to illustrate the proposed approach.

Authors who are presenting talks have a * after their name.

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