Pointwise Estimation of Anisotropic Regression Functions Using Wavelets with Data-Driven Selection Rule

Jia Chen and Junke Kou ()
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Jia Chen: School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, China
Junke Kou: School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China

Mathematics, 2023, vol. 12, issue 1, 1-10

Abstract: For nonparametric regression estimation, conventional research all focus on isotropic regression function. In this paper, a linear wavelet estimator of anisotropic regression function is constructed, the rate of convergence of this estimator is discussed in anisotropic Besov spaces. More importantly, in order to obtain an adaptive estimator, a regression estimator is proposed with scaling parameter data-driven selection rule. It turns out that our results attain the optimal convergence rate of nonparametric pointwise estimation.

Keywords: data-driven; anisotropic regression function; pointwise error; wavelets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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