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Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

Author

Listed:
  • Xingcai Zhou

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, China)

  • Guang Yang

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, China)

  • Yu Xiang

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, China)

Abstract

The paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the errors to be independently distributed. Quantile-wavelet estimation is robust to outliers or heavy-tailed data. The model is a dynamic time-varying model of nonlinear time series. A strong Bahadur order O 2 m n 3 / 4 ( log n ) 1 / 2 for the estimation is obtained under mild conditions. As applications, the rate of uniform strong convergence and the asymptotic normality are derived.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2321-:d:854641
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    References listed on IDEAS

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    1. Y. Andriyana & I. Gijbels, 2017. "Quantile regression in heteroscedastic varying coefficient models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 151-176, April.
    2. 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.
    3. Linyuan Li & Yimin Xiao, 2017. "Wavelet-based estimation of regression function with strong mixing errors under fixed design," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(10), pages 4824-4842, May.
    4. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    5. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    6. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    7. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    8. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    9. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    10. Xingcai Zhou & Fangxia Zhu, 2020. "Wavelet-M-Estimation for Time-Varying Coefficient Time Series Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-11, September.
    11. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    12. Guodong Xing & Shanchao Yang, 2019. "On the Bahadur representation of sample quantiles for ψ-mixing sequences and its application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(5), pages 1060-1072, March.
    13. Orbe, Susan & Ferreira, Eva & Rodriguez-Poo, Juan, 2005. "Nonparametric estimation of time varying parameters under shape restrictions," Journal of Econometrics, Elsevier, vol. 126(1), pages 53-77, May.
    14. 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.
    15. 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.
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