Estimation and inference in functional varying-coefficient single-index quantile regression models

We propose a flexible functional varying-coefficient single-index quantile regression model where the functional covariates of the linear part have time-varying coefficients and the single-index component offers great model flexibility in data analysis while circumventing the curse of dimensionality. The proposed model includes many existing quantile regression models for functional/longitudinal data as special cases. We use B-splines to estimate the link and coefficient functions. Under some mild conditions, we establish the asymptotic normality of the estimated index parameter vector, and obtain the convergence rates of the estimated link and coefficient functions. Moreover, we propose a score test to examine whether the effects of some covariates on the functional response are time-varying. Finally, we provide some numerical studies including Monte Carlo simulations and an empirical application to illustrate the proposed method.