Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 13, Number 1 (2019), 120-165.
Auxiliary information: the raking-ratio empirical process
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.
Electron. J. Statist., Volume 13, Number 1 (2019), 120-165.
Received: March 2018
First available in Project Euclid: 4 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G30: Order statistics; empirical distribution functions 62G20: Asymptotic properties
Secondary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles
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