## Bertrand Maillot, Christophe Chesneau

*Generalized regression estimation for continuous time processes with values in functional spaces*

Comment.Math.Univ.Carolin. 62,4 (2021) 461-481.**Abstract: **We consider two continuous time processes; the first one is valued in a semi-metric space, while the second one is real-valued. In some sense, we extend the results of F. Ferraty and P. Vieu in ``Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination" (2004), by establishing the convergence, with rates, of the generalized regression function when a real-valued continuous time response is considered. As corollaries, we deduce the convergence of the conditional distribution function as well as conditional quantiles. Note that a parametric rate of convergence in probability is reached while working with a naive kernel.

**Keywords:** continuous time process; regression function estimation; conditional distribution function

**DOI:** DOI 10.14712/1213-7243.2022.003

**AMS Subject Classification:** 62G07 62C05 62E20

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