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Results in Mathematics

, 74:128 | Cite as

Pointwise Wavelet Estimation of Regression Function Based on Biased Data

  • Huijun Guo
  • Junke KouEmail author
Article
  • 70 Downloads

Abstract

In this paper, we establish wavelet estimations on pointwise \(l^{p}(1\le p<\infty )\) risk for multivariate regression functions based on biased data. We firstly introduce a linear wavelet estimator and discuss the convergence rate of this estimator. In order to obtain an adaptive estimator, a nonlinear wavelet estimator is constructed by the hard thresholding method. It should be pointed out that the convergence rate of linear and nonlinear wavelet estimators coincide with the optimal convergence rate of pointwise nonparametric estimation.

Keywords

Pointwise adaptive biased regression estimation wavelets 

Mathematics Subject Classification

62G07 62G20 42C40 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewer for the important comments and suggestions. This paper is supported by Guangxi Natural Science Foundation (Nos. 2017GXNSFAA198194 and 2018GXNSFBA281076), Guangxi Science and Technology Project (Nos. Guike AD18281058 and Guike AD18281019), the Guangxi Young Teachers Basic Ability Improvement Project (Nos. 2018KY0212 and 2019KY0218) and Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceGuilin University of Electronic TechnologyGuilinPeople’s Republic of China

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