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Computational Statistics

, Volume 34, Issue 4, pp 1711–1740 | Cite as

Weighted composite quantile regression for single index model with missing covariates at random

  • Huilan LiuEmail author
  • Hu Yang
  • Changgen Peng
Original paper
  • 99 Downloads

Abstract

This paper considers weighted composite quantile estimation of the single-index model with missing covariates at random. Under some regularity conditions, we establish the large sample properties of the estimated index parameters and link function. The large sample properties of the parametric part show that the estimator with estimated selection probability have a smaller limiting variance than the one with the true selection probability. However, the large sample properties of the estimated link function indicate that whether weights were estimated or not has no effect on the asymptotic variance. Studies of simulation and the real data analysis are presented to illustrate the behavior of the proposed estimators.

Keywords

Horvitz–Thompson property Local linear regression Missing at random 

Notes

Acknowledgements

The authors sincerely thank the Editor, the Associate Editor and two Reviewers for their helpful comments and suggestions which lead to a significant improvement on this paper. Liu’s work is supported by the National Natural Science Foundation of China (Grant No. 11761020), China Postdoctoral Science Foundation(Grant No. 2017M623067), Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data(Grant No. 2017BDKFJJ030), Scientific Research Foundation for Young Talents of Department of Education of Guizhou Province(Grant No. 2017104), Science and Technology Foundation of Guizhou Province (Grant No. QKH20177222). Yang’s work is supported by the National Natural Science Foundation of China (Grant No. 11671059). Peng’s work is supported by the National Natural Science Foundation of China (Grant No. 61662009), Science and Technology Foundation of Guizhou Province (Grant No. QKH20183001).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Guizhou Provincial Key Laboratory of Public Big DataGuizhou UniversityGuiyangPeople’s Republic of China
  2. 2.College of Mathematics and StatisticsGuizhou UniversityGuiyangPeople’s Republic of China
  3. 3.College of Mathematics and StatisticsChongqing UniversityChongqingPeople’s Republic of China

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