  The main purpose of this paper is to investigate the strong approximation of
the integrated empirical process. More precisely, we obtain the exact rate of
the approximations by a sequence of weighted Brownian bridges and a weighted
Kiefer process. Our arguments are based in part on the Koml\'os, Major and
Tusn\'ady's results. Applications include the two-sample testing procedures
together with the change-point problems. We also consider the strong
approximation of the integrated empirical process when the parameters are
estimated. Finally, we study the behavior of the self-intersection local time
of the partial sum process representation of the integrated empirical process.
  Reference: Koml\'os, J., Major, P. and Tusn\'ady, G. (1975). An approximation
of partial sums of independent RV's and the sample DF. I. Z.
Wahrscheinlichkeitstheorie und Verw. Gebiete, 32, 111-131.
