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Strong consistency of wavelet estimators for errors-in-variables regression model

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  • Huijun Guo

    (Beijing University of Technology)

  • Youming Liu

    (Beijing University of Technology)

Abstract

This paper studies the strong consistency of some estimators for an errors-in-variables regression model. We first provide an extension of Meister’s theorem. Then, the same problem is dealt with under the Fourier-oscillating noises. Finally, we prove two strong consistency theorems for wavelet estimators corresponding to non-oscillating and Fourier-oscillating noises.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:1:d:10.1007_s10463-015-0529-6
    DOI: 10.1007/s10463-015-0529-6
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    References listed on IDEAS

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    1. 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.
    2. Ramazan Gencay & Nikola Gradojevic, 2009. "Errors-in-Variables Estimation with No Instruments," Working Paper series 30_09, Rimini Centre for Economic Analysis.
    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. 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.
    5. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    6. Li, Yongming & Yang, Shanchao & Zhou, Yong, 2008. "Consistency and uniformly asymptotic normality of wavelet estimator in regression model with associated samples," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2947-2956, December.
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    Cited by:

    1. 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.

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