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

AbstractLet {Xj}j = − ∞∞ be a vector-valued stationary process with a first-order univariate probability density f on Rd. We consider the recursive estimation of f(x) from n observations {Xj}j=1n which need not be independent. For processes {Xj}j = − ∞∞ which are asymptotically uncorrelated, we establish sharp rates for the almost sure convergence of kernel-type estimators fn(x)