Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong consistency and rates

Abstract

Let { X j } ∞ j =−∞ be a real-valued stationary process. Recursive kernel estimators of the joint probability density functions, of conditional probability densities, and of the conditional expectations of functionals of X j , given past behavior, are considered. Their strong consistency, along with rates, are established for processes { X j } satisfying various mixing conditions.