STRONG CONSISTENCY OF THE NEAREST NEIGHBOR-KERNEL ESTIMATORS OF CONDITIONAL DENSITY FUNCTION

Let （X,Y）, （X₁, Y₁）, …, （X_n, Y_n） be R^p×R^q-valued i.i.d, random vectors, and f（y|x） the conditional density function of Y, given X=x. Note that the existence of the density of （X, Y） is not assumed here. In this paper, we introduce the nearest neighborkernel estimator f_n（y|x） of f（y|x）, and establish the strong consistency of f_n（y|x） under some mild conditions.