Paper 2011/297 Original: eprint.iacr.org/2011/297 ↗
NEW STATISTICAL BOX-TEST AND ITS POWER
Abstract
In this paper, statistical testing of $N$ multinomial probabilities is studied and a new box-test, called \emph{Quadratic Box-Test}, is introduced. The statistics of the new test has $\chi^2_s$ limit distribution as $N$ and the number of trials $n$ tend to infinity, where $s$ is a parameter. The well-known empty-box test is a particular case for $s=1$. The proposal is quite different from Pearson's goodness-of-fit test, which requires fixed $N$ while the number of trials is growing, and linear box-tests. We prove that under some conditions on tested distribution the new test's power tends to $1$. That defines a wide region of non-uniform multinomial probabilities distinguishable from the uniform. For moderate $N$ an efficient algorithm to compute the exact values of the first kind error probability is devised.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2011-07-07: last updated
- 2011-06-08: published
- Short URL
- https://ia.cr/2011/297
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2011/297,
author = {Igor Semaev and Mehdi M. Hassanzadeh},
title = {NEW STATISTICAL BOX-TEST AND ITS POWER},
howpublished = {Cryptology {ePrint} Archive, Paper 2011/297},
year = {2011},
url = {https://eprint.iacr.org/2011/297}
}