Kernel density estimation under weak dependence with sampled data

Abstract

Kernel type estimators of the density of continuous time \r\nR\r\nd-valued stochastic processes are studied. Uniform strong consistency on \r\nR\r\nd of the estimators and their rates of convergence are obtained. The stochastic processes are assumed to satisfy the strong mixing condition and the sampling instants are random. It is shown that the estimators can attain the optimal L2 rates of convergence.