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Regression estimation under strong mixing data

Author

Listed:
  • Huijun Guo

    (Beijing University of Technology)

  • Youming Liu

    (Beijing University of Technology)

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.

Suggested Citation

  • Huijun Guo & Youming Liu, 2019. "Regression estimation under strong mixing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 553-576, June.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:3:d:10.1007_s10463-018-0653-1
    DOI: 10.1007/s10463-018-0653-1
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    References listed on IDEAS

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    1. Yogendra P. Chaubey & Esmaeil Shirazi, 2015. "On MISE of a Non linear Wavelet Estimator of the Regression Function Based on Biased Data under Strong Mixing," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 885-899, March.
    2. Shen, Jia & Xie, Yuan, 2013. "Strong consistency of the internal estimator of nonparametric regression with dependent data," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1915-1925.
    3. Yogendra P. Chaubey & Christophe Chesneau & Esmaeil Shirazi, 2013. "Wavelet-based estimation of regression function for dependent biased data under a given random design," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 53-71, March.
    4. Huijun Guo & Youming Liu, 2017. "Strong consistency of wavelet estimators for errors-in-variables regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 121-144, February.
    5. Chesneau, Christophe & Fadili, Jalal & Maillot, Bertrand, 2015. "Adaptive estimation of an additive regression function from weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 77-94.
    6. Raymond J. Carroll & Aurore Delaigle & Peter Hall, 2007. "Non‐parametric regression estimation from data contaminated by a mixture of Berkson and classical errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 859-878, November.
    7. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    8. Mokkadem, Abdelkader, 1988. "Mixing properties of ARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 309-315, September.
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