An adaptive estimation for covariate-adjusted nonparametric regression model

Feng Li, Lu Lin (), Yiqiang Lu and Sanying Feng
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Feng Li: Zhengzhou University
Lu Lin: Shandong University
Yiqiang Lu: PLA Strategic Support Force Information Engineering University
Sanying Feng: Zhengzhou University

Statistical Papers, 2021, vol. 62, issue 1, No 6, 93-115

Abstract: Abstract 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.

Keywords: Covariate-adjusted regression; Nonparametric estimation; Adaptability; Asymmetric distribution; Efficiency (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01084-0

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