  We study the empirical measure associated to a sample of size $n$ and
modified by $N$ iterations of the raking-ratio method. This empirical measure
is adjusted to match the true probability of sets in a finite partition which
changes each step. We establish asymptotic properties of the raking-ratio
empirical process indexed by functions as $n\rightarrow +\infty$, for $N$
fixed. We study nonasymptotic properties by using a Gaussian approximation
which yields uniform Berry-Esseen type bounds depending on $n, N$ and provides
estimates of the uniform quadratic risk reduction. A closed-form expression of
the limiting covariance matrices is derived as $N\rightarrow +\infty$. In the
two-way contingency table case the limiting process has a simple explicit
formula.
