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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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