Strong consistency and rates for recursive probability density estimators of stationary processes (Q1089711)

Authors's abstract: Let \(\{X_ j\}^{\infty}_{j=-\infty}\) be a vector-valued stationary process with a first-order univariate probability density f on \({\mathbb{R}}^ d\). Recursive estimation of f(x) from n not necessarily independent observations \(\{X_ j\}^ n_{j=1}\) is considered. For processes \(\{X_ j\}^{\infty}_{j=-\infty}\) which are asymptotically uncorrelated, sharp rates for the almost sure convergence of kernel-type estimators \(f_ n(x)\) are established.