Quantile estimation for a hybrid model of functional and varying coefficient regressions

We consider a hybrid of functional and varying-coefficient regression models for the analysis of mixed functional data. We propose a quantile estimation of this hybrid model as an alternative to the least square approach. Under regularity conditions, we establish the asymptotic normality of the proposed estimator. We show that the estimated slope function can attain the minimax convergence rate as in functional linear regression. A Monte Carlo simulation study and a real data application suggest that the proposed estimation is promising.