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Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors

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  • Zhou, Xing-cai
  • Lin, Jin-guan

Abstract

Consider the semiparametric regression model yi=xiTβ+g(ti)+εi for i=1,…,n, where xi∈Rp are the random design vectors, ti are the constant sequences on [0,1], β∈Rp is an unknown vector of the slop parameter, g is an unknown real-valued function defined on the closed interval [0,1], and the error random variables εi are coming from a stationary stochastic process, satisfying the strong mixing condition in some results. Under suitable conditions, we obtain expansions for the bias and the variance of wavelet estimators βˆn and gˆn(⋅) of β and g(⋅) respectively, prove their weak consistency, and establish the asymptotic normality and the Berry–Esseen bound of βˆn.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:251-270
    DOI: 10.1016/j.jmva.2013.08.006
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    References listed on IDEAS

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    Cited by:

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    2. Liwang Ding & Ping Chen & Yongming Li, 2020. "Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples," Statistical Papers, Springer, vol. 61(6), pages 2331-2349, December.
    3. Xuejun Wang & Xin Deng & Shuhe Hu, 2018. "On consistency of the weighted least squares estimators in a semiparametric regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 797-820, October.
    4. Nan Cheng & Chao Lu & Jibing Qi & Xuejun Wang, 2022. "Complete moment convergence for randomly weighted sums of extended negatively dependent random variables with application to semiparametric regression models," Statistical Papers, Springer, vol. 63(2), pages 397-419, April.
    5. Xuejun Wang & Yi Wu & Shuhe Hu & Nengxiang Ling, 2020. "Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models," Statistical Papers, Springer, vol. 61(3), pages 1147-1180, June.
    6. Lu Yang & Shigeyuki Hamori, 2020. "Forecasts of Value-at-Risk and Expected Shortfall in the Crude Oil Market: A Wavelet-Based Semiparametric Approach," Energies, MDPI, vol. 13(14), pages 1-27, July.
    7. Zhou, Xing-cai & Xu, Ying-zhi & Lin, Jin-guan, 2017. "Wavelet estimation in varying coefficient models for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 179-189.
    8. Xingcai Zhou & Guang Yang & Yu Xiang, 2022. "Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models," Mathematics, MDPI, vol. 10(13), pages 1-15, July.

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