Single-index composite quantile regression

Abstract

a b s t r a c tIn this paper, we extend the composite quantile regression (CQR) method to a single-index model. The unknown link function is estimated by local composite quantile regression and the parametric index is estimated through the linear composite quantile. It is shown that the proposed estimators are consistent and asymptotically normal. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.

Composite Quantile Regression for Nonparametric Model with Random Censored Data

“…They compared CQR with least squares and quantile regression, and the results showed that CQR outperformed both least squares and quantile regression. [8] considered CQR…”

Composite quantile regression for linear errors-in-variables models

“…Furthermore, the CQR estimator could be more efficient and sometimes arbitrarily more efficient than the least squares estimator. Other references about CQR method can see Kai, Li and Zou (2010), Zou (2011), Tang et al (2012a), Tang et al (2012b), Guo et al (2012) and Jiang et al (2012bJiang et al ( , 2012cJiang et al ( , 2013Jiang et al ( , 2014aJiang et al ( , 2014b. These nice theoretical properties of CQR in linear regression motivate us to consider linear errors-in-variables models based on CQR method so as to make the method of CQR more effective and convenient.…”

Penalized Single-Index Quantile Regression

“…A practical algorithm is introduced where the authors used the local linear QR to estimate the unknown link function and linear QR to estimate the parametric index. Jiang et al (2012) proposed the local linear composite QR estimator for a single-index model. Hua et al (2012) developed a Bayesian method for fitting models with a single-index using conditional QR.…”