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A0184
Title: Weighted composite quantile regression for single-index models Authors:  Rong Jiang - Donghua university (China) [presenting]
Abstract: A weighted composite quantile regression (WCQR) estimation is proposed for single-index models. For the parametric part, the WCQR is augmented by using a data-driven weighting scheme. With the error distribution unspecified, the proposed estimators share robustness with the quantile regression and achieve nearly the same efficiency as the semiparametric maximum likelihood estimator for a variety of error distributions including the Normal, Students t, Cauchy distributions, etc. Furthermore, based on the proposed WCQR, we use the adaptive-LASSO to study variable selection for parametric part in the single-index models. For the nonparametric part, the WCQR is augmented by combining the equal weighted estimators with possibly different weights. Because of the use of weights, the estimation bias is eliminated asymptotically. By comparing the asymptotic relative efficiency theoretically and numerically, the WCQR estimation all outperforms the CQR estimation and some other estimation methods. Under regularity conditions, the asymptotic properties of the proposed estimators are established. Simulation studies and two real data applications are conducted to illustrate the finite sample performance of the proposed methods.