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Optimal rates of convergence for nonparametric regression estimation under anisotropic Hölder condition

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  • Huijun Guo
  • Junke Kou

Abstract

In the multidimensional setting, we consider the nonparametric regression estimation with errors-in-variables. Both ordinary smooth noise and super smooth one are assumed for errors in the covariates. An anisotropic kernel estimator is provided based on a deconvolution technique. We study the pointwise estimation and obtain the optimal rates of convergence under the anisotropic Hölder condition.

Suggested Citation

  • Huijun Guo & Junke Kou, 2024. "Optimal rates of convergence for nonparametric regression estimation under anisotropic Hölder condition," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(2), pages 687-699, January.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:2:p:687-699
    DOI: 10.1080/03610926.2022.2091781
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