Paper 2011/297

NEW STATISTICAL BOX-TEST AND ITS POWER

Igor Semaev and Mehdi M. Hassanzadeh

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.

Note: A number of misprints are fixed, including one in the e-mail address. Some editorial work was applied.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown where it was published
Keywords
Hash-FunctionsStatistical TestingChi-square Goodness-of-fit TestAllocation ProblemEmpty-Box TestLinear Box-TestQuadratic Box-TestProbability of Errors
Contact author(s)
igor @ ii uib no
History
2011-07-07: revised
2011-06-08: received
See all versions
Short URL
https://ia.cr/2011/297
License
Creative Commons Attribution
CC BY

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},
      note = {\url{https://eprint.iacr.org/2011/297}},
      url = {https://eprint.iacr.org/2011/297}
}
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