Statistical analysis of prediction in functional polynomial quantile regression

We consider in this paper the quantile regression in a functional polynomial model, where the conditional quantile of a scalar response is modeled by a polynomial of functional predictor. It extends beyond the standard functional linear setting to accommodate more general functional polynomial model. A Tikhonov regularized functional polynomial quantile regression approach is introduced and investigated. By utilizing some techniques of empirical processes, we establish the explicit convergence rates of the prediction error of the proposed estimator under mild assumptions.