Empirical likelihood for quantile regression models with response data missing at random

S. Luo, and Shuxia Pang. "Empirical likelihood for quantile regression models with response data missing at random." Open Mathematics 15.1 (2017): 317-330. <http://eudml.org/doc/288051>.

@article{S2017,
abstract = {This paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood ratios including quantile empirical likelihood ratio with complete-case data, weighted quantile empirical likelihood ratio and imputed quantile empirical likelihood ratio are defined for the regression parameters. Then, a bias-corrected quantile empirical log-likelihood ratio is constructed for the mean of the response variable for a given quantile level. It is proved that these quantile empirical log-likelihood ratios are asymptotically χ2 distribution. Furthermore, a class of estimators for the regression parameters and the mean of the response variable are constructed, and the asymptotic normality of the proposed estimators is established. Our results can be used directly to construct the confidence intervals (regions) of the regression parameters and the mean of the response variable. Finally, simulation studies are conducted to assess the finite sample performance and a real-world data set is analyzed to illustrate the applications of the proposed method.},
author = {S. Luo, Shuxia Pang},
journal = {Open Mathematics},
keywords = {Quantile regression; Empirical likelihood; Missing response data; Confidence interval; quantile regression; empirical likelihood; missing response data; confidence interval},
language = {eng},
number = {1},
pages = {317-330},
title = {Empirical likelihood for quantile regression models with response data missing at random},
url = {http://eudml.org/doc/288051},
volume = {15},
year = {2017},
}

TY - JOUR
AU - S. Luo
AU - Shuxia Pang
TI - Empirical likelihood for quantile regression models with response data missing at random
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 317
EP - 330
AB - This paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood ratios including quantile empirical likelihood ratio with complete-case data, weighted quantile empirical likelihood ratio and imputed quantile empirical likelihood ratio are defined for the regression parameters. Then, a bias-corrected quantile empirical log-likelihood ratio is constructed for the mean of the response variable for a given quantile level. It is proved that these quantile empirical log-likelihood ratios are asymptotically χ2 distribution. Furthermore, a class of estimators for the regression parameters and the mean of the response variable are constructed, and the asymptotic normality of the proposed estimators is established. Our results can be used directly to construct the confidence intervals (regions) of the regression parameters and the mean of the response variable. Finally, simulation studies are conducted to assess the finite sample performance and a real-world data set is analyzed to illustrate the applications of the proposed method.
LA - eng
KW - Quantile regression; Empirical likelihood; Missing response data; Confidence interval; quantile regression; empirical likelihood; missing response data; confidence interval
UR - http://eudml.org/doc/288051
ER -