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. 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.

Domaines: Théorie [stat.TH]

Mickael Albertus, Philippe Berthet. Auxiliary information : the raking-ratio empirical process. 2018. ⟨hal-01736276v1⟩