Abstract: In this paper, the nonparameteric estimations of conditional functional and its derivatives are studied. Strong uniform convergence rates are proved to be optimal for kernel type estimator and weighted estimator of conditional functional in the random design and the fixed design,under certain conditions. Various previous results in the literature (for example Härdle etal. (1988).Severini and Wong (1992) are extended and sharpened.

Key words: Conditional functional, Strong uniform convergence, Kernel estimators, Weighted estimators, Optimal convergence rates