ABSTRACT
Linear quantile regression with real response and functional covariate is considered by K. Kato and Cardot et al. Nonparametric quantile regression with real response and functional covariate is investigated in Ferraty and Vieu and Gardes et al. Semiparametric quantile regression with real response and functional covariate is explored in Chen and Muller. Nonparametric quantile regression with finite-dimensional response and functional covariate is studied in Chaouch and Laib. The quantile regression for Banach-valued response developed in this section can also be used to investigate the presence of heteroskedasticity in the data. Consistency of spatial quantiles in a Banach space was stated in an unconditional setup. An estimate of the conditional spread based on regression quantiles has been developed. The consistency of this conditional spread measure follows from the consistency of the conditional quantile estimates.
