A Note on the Strong Approximation of the Smoothed Empirical Process of α-mixing Sequences

Abstract

A strong approximation of the smoothed empirical process of strictly stationary α-mixing random variables by a sequence of iid Gaussian processes will be studied. Here, the smoothing is done via kernel density estimators. No assumptions are made on the support of the kernel; in fact, our main results are stated for kernels with possibly an infinite support.