Weak convergence of marked empirical processes in a Hilbert space and its applications

Abstract

We discuss goodness-of-fit tests for stationary ergodic processes based on limit theorems for marked empirical processes viewed as elements of an $L^{2}$ space. Our limit theorems cover a weighted process that enables an Anderson–Darling-type test statistic for the goodness-of-fit tests to be proposed. The procedures presented for these goodness-of-fit tests are novel.