ARBITRARY FUNCTIONAL GLIVENKO-CANTELLI CLASSES AND APPLICATIONS TO DIFFERENT TYPES OF DEPENDENCE
Using a general strong law of large numbers proved by Sangaré and Lo [14] and the entropy numbers, we provide functional Glivenko-Cantelli (GC) classes for arbitrary stationary real-valued random variables (rrv’s). Next, the general results are particularized for different types of dependence (association, φ-mixing, in particular) and compared with available results in the literature.
association, φ-mixing, stationarity, entropy number, Glivenko-Cantelli class.