Title: Raking-ratio empirical process with auxiliary information learning,
Abstract: The raking-ratio method is a statistical and computational method which
adjusts the empirical measure to match the true probability of sets in a finite
partition. We study the asymptotic behavior of the raking-ratio empirical
process indexed by a class of functions when the auxiliary information is given
by the learning of the probability of sets in partitions from another sample
larger than the sample of the statistician. Under some metric entropy
hypothesis and conditions on the size of the independent samples, we establish
the strong approximation of this process with estimated auxiliary information
and show in particular that weak convergence is the same as the classical
raking-ratio empirical process. We also give possible statistical applications
of these results like strengthening the $Z$-test and the chi-square goodness of
fit test.