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A Simple Algorithm for Exact Multinomial Tests

Resin, Johannes 1
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)

Abstract:

This work proposes a new method for computing acceptance regions of exact multinomial tests. From this an algorithm is derived, which finds exact p-values for tests of simple multinomial hypotheses. Using concepts from discrete convex analysis, the method is proven to be exact for various popular test statistics, including Pearson’s Chi-square and the log-likelihood ratio. The proposed algorithm improves greatly on the naive approach using full enumeration of the sample space. However, its use is limited to multinomial distributions with a small number of categories, as the runtime grows exponentially in the number of possible outcomes. The method is applied in a simulation study, and uses of multinomial tests in forecast evaluation are outlined. Additionally, properties of a test statistic using probability ordering, referred to as the “exact multinomial test” by some authors, are investigated and discussed. The algorithm is implemented in the accompanying R package ExactMultinom. Supplementary materials for this article are available online.


Verlagsausgabe §
DOI: 10.5445/IR/1000151826
Veröffentlicht am 24.10.2022
Originalveröffentlichung
DOI: 10.1080/10618600.2022.2102026
Scopus
Zitationen: 1
Web of Science
Zitationen: 1
Dimensions
Zitationen: 3
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 1061-8600, 1537-2715
KITopen-ID: 1000151826
Erschienen in Journal of Computational and Graphical Statistics
Verlag Taylor and Francis
Band 32
Heft 2
Seiten 539-550
Vorab online veröffentlicht am 21.09.2022
Schlagwörter Acceptance regions, Goodness-of-fit test, Log-likelihood ratio, Pearson’s Chi-square, Probability mass statistic, R software
Nachgewiesen in Dimensions
Web of Science
Scopus
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