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Regression estimation under strong mixing data

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Abstract

This paper studies multivariate wavelet regression estimators with errors-in-variables under strong mixing data. We firstly prove the strong consistency for non-oscillating and Fourier-oscillating noises. Then, a convergence rate is provided for non-oscillating noises, when an estimated function has some smoothness. Finally, the consistency and convergence rate are discussed for a practical wavelet estimator.

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Acknowledgements

This paper is supported by the Beijing Natural Science Foundation (No. 1172001) and the National Natural Science Foundation of China (No. 11771030). The authors would like to thank the referees for their important comments and suggestions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing University of Technology, Pingle Yuan 100, Beijing, 100124, People’s Republic of China

    Huijun Guo & Youming Liu

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  1. Huijun Guo
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  2. Youming Liu
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Correspondence to Youming Liu.

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Guo, H., Liu, Y. Regression estimation under strong mixing data. Ann Inst Stat Math 71, 553–576 (2019). https://doi.org/10.1007/s10463-018-0653-1

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  • DOI: https://doi.org/10.1007/s10463-018-0653-1

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