pp 1–25 | Cite as

Identification and estimation in quantile varying-coefficient models with unknown link function

  • Lili Yue
  • Gaorong LiEmail author
  • Heng Lian
Original Paper


In this paper, we consider the estimation problem of quantile varying-coefficient models when the link function is unspecified, which significantly expands the existing works on varying-coefficient models with unspecified link function focusing only on mean regression. We provide new identification conditions which are weaker than existing ones. Under these identification conditions, we use polynomial splines to estimate both the varying coefficients and the link functions and establish the convergence rate of the estimator. Our simulation studies and a real data application illustrate the finite sample performance of the estimators.


Asymptotic property B-splines Check loss minimization Single-index models Quantile regression 

Mathematics Subject Classification

62G08 62G20 62G35 



The authors want to sincerely thank the Editor-in-Chief Professor Ugarte, an Associate Editor, and two referees for their insightful comments that greatly improved the manuscript. The research of Heng Lian is partially supported by City University of Hong Kong Startup Grant 7200521, Hong Kong RGC general research fund 11301718, and Project 11871411 from NSFC and the Shenzhen Research Institute, City University of Hong Kong. Gaorong Li and Lili Yue’s research was supported by the National Natural Science Foundation of China (11871001) and the Beijing Natural Science Foundation (1182003).


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Beijing Institute for Scientific and Engineering ComputingBeijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.Department of MathematicsCity University of Hong KongKowloonHong Kong

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