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Statistical Methods & Applications

, Volume 27, Issue 4, pp 667–688 | Cite as

Wavelet regression estimations with strong mixing data

  • Junke Kou
  • Youming Liu
Original Paper
  • 73 Downloads

Abstract

Using a wavelet basis, we establish in this paper upper bounds of wavelet estimation on \( L^{p}({\mathbb {R}}^{d}) \) risk of regression functions with strong mixing data for \( 1\le p<\infty \). In contrast to the independent case, these upper bounds have different analytic formulae for \(p\in [1, 2]\) and \(p\in (2, +\infty )\). For \(p=2\), it turns out that our result reduces to a theorem of Chaubey et al. (J Nonparametr Stat 25:53–71, 2013); and for \(d=1\) and \(p=2\), it becomes the corresponding theorem of Chaubey and Shirazi (Commun Stat Theory Methods 44:885–899, 2015).

Keywords

Regression estimation \(L^{p}\) risk Convergence rate Strong mixing Wavelet 

Mathematics Subject Classification

62G07 42C40 62G20 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China [11771030] and the Beijing Natural Science Foundation [1172001]. The authors would like to thank professor Wenqing Xu for his suggestions in writing this manuscript, and the referees for their comments which improve the manuscript.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsBeijing University of TechnologyBeijingPeople’s Republic of China

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