Single-index composite quantile regression with heteroscedasticity and general error distributions

Abstract

It is known that composite quantile regression (CQR) could be much more efficient and sometimes arbitrarily more efficient than the least squares estimator. Based on CQR method, we propose a weighted CQR (WCQR) method for singleindex models with heteroscedasticity and general error distributions. Because of the use of weights, the estimation bias is eliminated asymptotically. By comparing asymptotic relative efficiency, WCQR estimation outperforms the CQR estimation and least squares estimation. The simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.

Composite quantile regression for massive datasets

“…Kai et al (2011) studied semiparametric CQR estimates for the semiparametric varying-coefficient partially linear model. For other references about CQR method see Tang et al (2012Tang et al ( , 2015, Jiang et al ( , 2013Jiang et al ( , 2014Jiang et al ( , 2015Jiang et al ( , 2016aJiang et al ( , 2016bJiang et al ( , 2018, Ning and Tang (2014), Zhang et al (2016), Tian et al (2016), and so on. These nice theoretical properties of CQR in linear regression motivate us to consider CQR method for massive datasets.…”

Single-index composite quantile regression for massive data

“…Remark 2.3: For Theorem 2.1, the proposed estimator achieves the same efficiency as the iterative CQR estimator proposed by Jiang et al (2012). The results of Theorem 2.2 are thus the same as those of Theorem 5 in Jiang et al (2016b). Thus, the selection of the optimal bandwidth h can be found in Jiang et al (2016b).…”

“…After obtaining the estimator γ of γ 0 in model (1.1), we can estimate g 0 (•) in model (1.1). We used the weighted local CQR (WLCQR) proposed by Jiang et al (2016b), which is valid without a symmetric error condition. For any given point u, the final estimate of g 0 (•) is…”

Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information

“…Remark 2. If we simply use equal weights in (14), then the resulting unweighted quantile average estimator for m (t 0 ) has the asymptotic normality in Theorem 2 with J ω (q) replaced by:…”

“…Recently, many researchers applied the COR method to other various models under different data cases. It can be referred but not limited to [13][14][15][16][17][18][19].…”