Auxiliary information : the raking-ratio empirical process
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We study the empirical measure associated to a sample of size n and modified by N iterations of the raking-ratio method. The 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→ +∞, for N fixed. A closed-form expression of the limiting covariance matrices is derived as N→ +∞. The nonasymptotic Gaussian approximation we use also yields uniform Berry-Esseen type bounds in n, N and sharp estimates of the uniform quadratic risk reduction. In the two-way contingency table formulas characterizing the limiting process are very simple.
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