Weak convergence of the empirical process and the rescaled empirical distribution function in the Skorokhod product space

Dietmar Ferger, Daniel Vogel

We prove the asymptotic independence of the empirical process ${\alpha }_n=\sqrt{n}(F_n-F)$ and the rescaled empirical distribution function ${\beta }_n=n(F_n(\tau +\frac{\cdot }{n})-F_n(\tau ))$,…