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Berry-Esseen bounds for wavelet estimator in a regression model with linear process errors

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  • Li, Yongming
  • Wei, Chengdong
  • Xing, Guodong

Abstract

In this paper, we derive the Berry-Esseen bounds of the wavelet estimator for a nonparametric regression model with linear process errors generated by [phi]-mixing sequences. As application, by the suitable choice of some constants, the convergence rate O(n-1/6) of uniformly asymptotic normality of the wavelet estimator is obtained. Our results generalize some known results in the literature.

Suggested Citation

  • Li, Yongming & Wei, Chengdong & Xing, Guodong, 2011. "Berry-Esseen bounds for wavelet estimator in a regression model with linear process errors," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 103-110, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:103-110
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    References listed on IDEAS

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    1. Yang, Shanchao, 2003. "Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 101-110, April.
    2. Kim, Tae-Sung & Ko, Mi-Hwa, 2008. "Complete moment convergence of moving average processes under dependence assumptions," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 839-846, May.
    3. 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.
    4. Georgiev, Alexander A., 1988. "Consistent nonparametric multiple regression: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 100-110, April.
    5. Schick, Anton & Wefelmeyer, Wolfgang, 2006. "Pointwise convergence rates and central limit theorems for kernel density estimators in linear processes," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1756-1760, October.
    6. Chen, Pingyan & Hu, Tien-Chung & Volodin, Andrei, 2009. "Limiting behaviour of moving average processes under [phi]-mixing assumption," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 105-111, January.
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    Cited by:

    1. Zhou, Xing-cai & Lin, Jin-guan, 2013. "Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 251-270.
    2. Xin Deng & Xuejun Wang & Yi Wu, 2021. "The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors," Statistical Papers, Springer, vol. 62(2), pages 963-984, April.
    3. Claudio Durastanti, 2016. "Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 651-673, November.

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