The main objective of this paper is to estimate the conditional cumulative distribution using the nonparametric kernel method for a surrogated scalar response variable given a functional random one. We introduce the new kernel type estimator for the conditional cumulative distribution function (cond-cdf) of this kind of data. Afterward, we estimate the quantile by inverting this estimated cond-cdf and state the asymptotic properties. The uniform almost complete convergence (with rate) of the kernel estimate of this model and the quantile estimator is established. Finally, a simulation study completed to show how our methodology can be adopted.
Metmous, Imane; Attouch, Mohammed K.; Mechab, Boubaker; and Merouan, Torkia
Nonparametric Estimation of the Conditional Distribution Function For Surrogate Data by the Regression Model,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
1, Article 4.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss1/4