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Asymptotic normality of a wavelet estimator for asymptotically negatively associated errors

Author

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  • Tang, Xufei
  • Xi, Mengmei
  • Wu, Yi
  • Wang, Xuejun

Abstract

In this paper, we consider the nonparametric regression model Yni=g(ti)+εni,1≤i≤n and n≥1, where {ti} are non-random design points, and g(⋅) is an unknown Borel measurable function defined on [0, 1]. Under some general conditions, we study the asymptotic normality of the wavelet estimator of g(⋅), where the random errors {εni} are asymptotically negatively associated (ANA, for short) random variables. In addition, a simulation study is provided to evaluate the finite sample performance of the wavelet estimator.

Suggested Citation

  • Tang, Xufei & Xi, Mengmei & Wu, Yi & Wang, Xuejun, 2018. "Asymptotic normality of a wavelet estimator for asymptotically negatively associated errors," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 191-201.
    • Handle: RePEc:eee:stapro:v:140:y:2018:i:c:p:191-201
    DOI: 10.1016/j.spl.2018.04.024
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    Cited by:

    1. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2022. "Universal Local Linear Kernel Estimators in Nonparametric Regression," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    2. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2024. "Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency," Mathematics, MDPI, vol. 12(12), pages 1-23, June.

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