Raking-ratio empirical process with auxiliary information learning
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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.
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