Statistical Papers

, Volume 60, Issue 3, pp 747–760 | Cite as

Testing for parametric component of partially linear models with missing covariates

  • Zhangong Zhou
  • Linjun TangEmail author
Regular Article


This paper considers the testing problem of partially linear models with missing covariates. The inverse probability weighted restricted estimator for the parametric component under linear constraint is derived and proven to share asymptotically normal distribution. To test the linear constraint, we construct two test statistics based on the the Lagrange multiplier and the empirical likelihood methods. The limiting distributions of the resulting test statistics are both standard chi-squared distributions under the null hypothesis. Simulation studies and a real data analysis are conducted to illustrate relevant performances.


Partially linear model Missing covariates Restricted estimator Lagrange multiplier Empirical likelihood ratio 



The authors thank the Editor and referees for the helpful comments and suggestions which greatly improved the paper. The Project Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LY15A010019).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of StatisticsJiaxing UniversityJiaxingChina

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