THE CONSISTENCY OF THE KERNEL ESTIMATION OF THE FUNCTION CONDITIONAL DENSITY FOR ASSOCIATED DATA IN HIGH-DIMENSIONAL STATISTICS

Abstract

The purpose of the present paper is to investigate by the kernel method a nonparametric estimate of the conditional density function of a scalar response variable given a random variable taking values in a separable real Hilbert space when the observations are quasi-associated dependent. Under some general conditions, we establish the pointwise almost complete consistencies with rates of this estimator. The principal aim is to investigate of the convergence rate of the proposed estimator.