Auxiliary information : the raking-ratio empirical process

Mickael Albertus (1) , Philippe Berthet (2)

1 UT3 - Université Toulouse III - Paul Sabatier
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Théorie [stat.TH]

Mickael Albertus, Philippe Berthet. Auxiliary information : the raking-ratio empirical process. Electronic Journal of Statistics , 2019, 13 (1), pp.120-165. ⟨hal-01736276v2⟩