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

• Autorzy: S. Luo , Shuxia Pang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Quantile regression; Empirical likelihood; Missing response data; Confidence interval

Kategorie tematyczne

• 62G20: Asymptotic properties
• 62G05: Estimation
• 60G42: Martingales with discrete parameter

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 317-330

Daty

wydano

2017-01-01

otrzymano

2016-06-28

zaakceptowano

2017-01-03

online

2017-03-27

Twórcy

autor

S. Luo

• School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048,
• School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049,

autor

Shuxia Pang

• School of Computer and Communication, Lanzhou University of Technology, Lanzhou, Gansu, 730000,

Identyfikatory

DOI

10.1515/math-2017-0028