Abstract:

The paper studies asymptotic behaviour of special type of empirical processes, inspired by specific properties of empirical distribution functions. The problem of convergence in distribution is discussed in Theorem 1. The relevant and more useful result of Theorem 2 establishes convergence in the space $D$. Section 2 discusses possible consequences if empirical distribution functions in a regression model are considered. An example indicates that the space $D$ is not sufficient to study the convergence even if empirical distributions of simple processes are considered.