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A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure

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  • Zhou, Xing-cai
  • Lin, Jin-guan

Abstract

Consider the wavelet estimator of a nonparametric regression model with repeated measurements under martingale difference error’s structure for exhibiting dependence among the units, and to avoid as far as possible any assumptions among the observations within the same unit. We show the moment consistency, the strong consistency and the strong convergence rate of the wavelet estimator, and establish its asymptotic normality.

Suggested Citation

  • Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1914-1922
    DOI: 10.1016/j.spl.2012.06.028
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    References listed on IDEAS

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    1. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Testing the martingale difference hypothesis using integrated regression functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2278-2294, December.
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    4. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
    5. Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    6. Bercu, B., 2004. "On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 157-173, May.
    7. Roussas, George G., 1989. "Consistent regression estimation with fixed design points under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 41-50, May.
    8. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    9. Poghosyan, S. & Roelly, S., 1998. "Invariance principle for martingale-difference random fields," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 235-245, June.
    10. Fraiman, Ricardo & Iribarren, Gonzalo Pérez, 1991. "Nonparametric regression estimation in models with weak error's structure," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 180-196, May.
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