Nonparametric Estimation of the Conditional Distribution Function For Surrogate Data by the Regression Model

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