Asymptotic Normality of the Nearest Neighbor-Kernel Estimator of Conditional Density

Let （X,Y） be R^p×R^q-valued random vector, and f（y|x） be the conditional density function of Y given X. In 1, the nearest neighbor-kernel estimator f_n（y|x） of f（y|x） was introduced, and the strong consistency of f_n（y|x） was proved. In the paper, the asymptotic normality of f_n（y|x） is obtained under some moderate conditions.