Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

Xingcai Zhou, Guang Yang and Yu Xiang
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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

Mathematics, 2022, vol. 10, issue 13, 1-15

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.

Keywords: quantile-wavelet; nonparametric estimation; time-varying coefficient; Bahadur representation; strong mixing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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