Electronic Journal of Statistics

Auxiliary information: the raking-ratio empirical process

Mickael Albertus and Philippe Berthet

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 120-165.

Dates
Received: March 2018
First available in Project Euclid: 4 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1546570944

Digital Object Identifier
doi:10.1214/18-EJS1526

Mathematical Reviews number (MathSciNet)
MR3896148

Zentralblatt MATH identifier
1411.62028

Subjects
Primary: 62G30: Order statistics; empirical distribution functions 62G20: Asymptotic properties
Secondary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles

Keywords
Raking-ratio method empirical processes strong approximation nonparametric statistics auxiliary information Sinkhorn algorithm

Rights
Creative Commons Attribution 4.0 International License.

Citation

Albertus, Mickael; Berthet, Philippe. Auxiliary information: the raking-ratio empirical process. Electron. J. Statist. 13 (2019), no. 1, 120--165. doi:10.1214/18-EJS1526. https://projecteuclid.org/euclid.ejs/1546570944


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