Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach

  • Weihua Zhao
  • Jianbo Li
  • Heng Lian


We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset.


Asymptotic normality Bias-corrected estimating equations Check loss Empirical processes Single-index model 



We sincerely thank the AE and two anonymous reviewers for their insightful comments which have led to significant improvement of the paper. The research of Zhao was supported in part by National Social Science Fund of China (15BTJ027), and the research of Lian was supported by a start up Grant (No. 7200521/MA) from the City University of Hong Kong.


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  1. 1.School of ScienceNantong UniversityNantongP. R. China
  2. 2.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouP. R. China
  3. 3.Department of MathematicsCity University of Hong KongKowloon TongHong Kong

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