Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models

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.