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2019 Auxiliary information: the raking-ratio empirical process
Mickael Albertus, Philippe Berthet
Electron. J. Statist. 13(1): 120-165 (2019). DOI: 10.1214/18-EJS1526

Abstract

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.

Citation

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Mickael Albertus. Philippe Berthet. "Auxiliary information: the raking-ratio empirical process." Electron. J. Statist. 13 (1) 120 - 165, 2019. https://doi.org/10.1214/18-EJS1526

Information

Received: 1 March 2018; Published: 2019
First available in Project Euclid: 4 January 2019

zbMATH: 1411.62028
MathSciNet: MR3896148
Digital Object Identifier: 10.1214/18-EJS1526

Subjects:
Primary: 62G20, 62G30
Secondary: 60F05, 60F17

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Vol.13 • No. 1 • 2019
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