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Computational Statistics

, Volume 33, Issue 2, pp 659–674 | Cite as

Robust empirical likelihood for partially linear models via weighted composite quantile regression

  • Peixin Zhao
  • Xiaoshuang Zhou
Original Paper
  • 166 Downloads

Abstract

In this paper, we investigate robust empirical likelihood inferences for partially linear models. Based on weighted composite quantile regression and QR decomposition technology, we propose a new estimation method for the parametric components. Under some regularity conditions, we prove that the proposed empirical log-likelihood ratio is asymptotically chi-squared, and then the confidence intervals for the parametric components are constructed. The resulting estimators for parametric components are not affected by the nonparametric components, and then it is more robust, and is easy for application in practice. Some simulations analysis and a real data application are conducted for further illustrating the performance of the proposed method.

Keywords

Weighted composite quantile regression Empirical likelihood Partially linear model QR decomposition 

Notes

Acknowledgements

This research is supported by the Chongqing Research Program of Basic Theory and Advanced Technology (cstc2016jcyjA0151), the Social Science Planning Project of Chongqing (2015PY24), the Fifth Batch of Excellent Talent Support Program for Chongqing Colleges and University (2017-35-16), and the Scientific Research Foundation of Chongqing Technology and Business University (2015-56-06).

References

  1. Bradic J, Fan J (2011) Penalized composite quasi-likelihood for ultrahigh dimensional variable selection. J R Stat Soc Ser B 73:325–349MathSciNetCrossRefGoogle Scholar
  2. Fan J, Li R (2004) New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. J Am Stat Assoc 99:710–723MathSciNetCrossRefzbMATHGoogle Scholar
  3. Huang JT, Zhao PX (2017) QR decomposition based orthogonality estimation for partially linear models with longitudinal data. J Comput Appl Math 321:406–415MathSciNetCrossRefzbMATHGoogle Scholar
  4. Jiang Y, Li H (2014) Penalized weighted composite quantile regression in the linear regression model with heavy-tailed autocorrelated errors. J Korean Stat Soc 43:531–543MathSciNetCrossRefzbMATHGoogle Scholar
  5. Jiang X, Jiang J, Song X (2012) Oracle model selection for nonlinear models based on weighted composite quantile regression. Stat Sin 22:1479–1506MathSciNetzbMATHGoogle Scholar
  6. Jiang J, Jiang X, Song X (2014) Weighted composite quantile regression estimation of DTARCH models. Econom J 17:1–23MathSciNetCrossRefGoogle Scholar
  7. Jiang R, Qian W, Zhou Z (2016) Weighted composite quantile regression for single-index models. J Multivar Anal 148:34–48MathSciNetCrossRefzbMATHGoogle Scholar
  8. Lee AJ, Scott AJ (1986) Ultrasound in ante-natal diagnosis. In: Brook RJ, Arnold GC, Hassard TH, Pringle RM (eds) The fascination of statistics. Marcel Dekker, New York, pp 277–293Google Scholar
  9. Liang H, Härdle W, Carroll RJ (1999) Estimation in a simiparametric partially linear errors-in-variables model. Ann Stat 27:1519–1535CrossRefzbMATHGoogle Scholar
  10. Liang H, Wang S, Carroll RJ (2007) Partially linear models with missing response variables and error-prone covariates. Biometrika 94:185–198MathSciNetCrossRefzbMATHGoogle Scholar
  11. Owen AB (1990) Empirical likelihood ratio confidence regions. Ann Stat 18:90–120MathSciNetCrossRefzbMATHGoogle Scholar
  12. Schumaker LL (1981) Spline function. Wiley, New YorkzbMATHGoogle Scholar
  13. Seber GAF, Wild CJ (1989) Nonlinear regression. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  14. Silverman BW (1986) Density estimation. Chapman and Hall, LondonCrossRefzbMATHGoogle Scholar
  15. Wang HJ, Zhu Z (2011) Empirical likelihood for quantile regression models with longitudinal data. J Stat Plan Inference 141:1603–1615MathSciNetCrossRefzbMATHGoogle Scholar
  16. Xu G, Wang S, Huang JZ (2014) Focused information criterion and model averaging basedon weighted composite quantile regression. Scand J Stat 41:365–381MathSciNetCrossRefzbMATHGoogle Scholar
  17. Xue LG (2009) Empirical likelihood for linear models with missing responses. J Multivar Anal 100:1353–1366MathSciNetCrossRefzbMATHGoogle Scholar
  18. Xue LG, Zhu LX (2007) Empirical likelihood semiparametric regression analysis for longitudinal data. Biometrika 94:921–937MathSciNetCrossRefzbMATHGoogle Scholar
  19. Yan L, Chen X (2014) Empirical likelihood for partly linear models with errors in all variables. J Multivar Anal 130:275–288MathSciNetCrossRefzbMATHGoogle Scholar
  20. Yang H, Lv J, Guo C (2015) Weighted composite quantile regression estimation and variable selection for varying coefficient models with heteroscedasticity. J Korean Stat Soc 44:77–94MathSciNetCrossRefzbMATHGoogle Scholar
  21. Zhao PX, Xue LG (2010) Empirical likelihood inferences for semiparametric varying coefficient partially linear models with longitudinal data. Commun Stat Theory Methods 39:1898–1914MathSciNetCrossRefzbMATHGoogle Scholar
  22. Zhao PX, Tang XR (2016) Imputation based statistical inference for partially linear quantile regression models with missing responses. Metrika 79:991–1009MathSciNetCrossRefzbMATHGoogle Scholar
  23. Zhao PX, Zhou XS, Lin L (2015) Empirical likelihood for composite quantile regression modeling. J Appl Math Comput 48:321–333MathSciNetCrossRefzbMATHGoogle Scholar
  24. Zou H, Yuan M (2008) Composite quantile regression and the oracle model selection theory. Ann Stat 36:1108–1126MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChongqing Technology and Business UniversityChongqingChina
  2. 2.School of Mathematical SciencesDezhou UniversityDezhouChina

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