Weak convergence for empirical processes of associated sequences
Weak convergence of linear rank statistics
Weak Hölder convergence of processes with application to the perturbed empirical process
We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample under a natural assumption about the regularity of the marginal distribution function F of the...