Recursive density estimation under dependence

Recursive estimators of the density of weakly dependent random variables are studied under certain absolute regularity and strong mixing conditions. Uniform strong consistency of the density estimators is established, and their rates of convergence are obtained. This study is concerned more with the almost sure uniform consistency of a sequence and its rate of convergence than with pointwise convergence. Since parameter estimation in time-series analysis is often carried out under the Gaussian assumption, it is useful to check whether or not the density of a time series is Gaussian or nearly so. The method of proof used here is based on approximations of absolutely regular and strong mixing random variables (RVs) by independent RVs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>