On smoothed probability density estimation for stationary processes

Aspects of estimation of the (marginal) probability density for a stationary sequence or continuous parameter process, are considered in this paper. Consistency and asymptotic distributional results are obtained using a class of smoothed function estimators including those of kernel type, under various decay of dependence conditions for the process. Some of the consistency results contain convergence rates which appear to be more delicate than those previously available, even for i.i.d. sequences.