An adaptive estimation for covariate-adjusted nonparametric regression model

  • Feng Li
  • Lu Lin
  • Yiqiang Lu
  • Sanying Feng
Regular Article


For covariate-adjusted nonparametric regression model, an adaptive estimation method is proposed for estimating the nonparametric regression function. Compared with the procedures introduced in the existing literatures, the new method needs less strict conditions and is adaptive to covariate-adjusted nonparametric regression with asymmetric variables. More specifically, when the distributions of the variables are asymmetric, the new procedures can gain more efficient estimators and recover data more accurately by elaborately choosing proper weights; and for the symmetric case, the new estimators can obtain the same asymptotic properties as those obtained by the existing method via designing equal bandwidths and weights. Simulation studies are carried out to examine the performance of the new method in finite sample situations and the Boston Housing data is analyzed as an illustration.


Covariate-adjusted regression Nonparametric estimation Adaptability Asymmetric distribution Efficiency 



The research was supported by NNSF Project (U1404104, 11501522, 11601283 and 11571204) of China, China Social Science Fund 18BTJ021 and a Natural Science Project of Zhengzhou University.


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Copyright information

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

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouChina
  2. 2.Zhongtai Securities Institute for Financial StudiesShandong UniversityJinanChina
  3. 3.School of StatisticsQufu Normal UniversityQufuChina
  4. 4.PLA Strategic Support Force Information Engineering UniversityZhengzhouChina

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