Geodesic
Generalized regression estimation for continuous time processes with values in functional spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 4, pp. 461-481.

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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.
DOI : 10.14712/1213-7243.2022.003
Classification : 62C05, 62E20, 62G07
Keywords: continuous time process; regression function estimation; conditional distribution function 
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Maillot, Bertrand; Chesneau, Christophe. Generalized regression estimation for continuous time processes with values in functional spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 4, pp. 461-481. doi : 10.14712/1213-7243.2022.003. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.003/

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