A simple algorithm for exact multinomial tests

• Verfasst von: Resin, Johannes [VerfasserIn]
• Titel: A simple algorithm for exact multinomial tests
• Verf.angabe: Johannes Resin
• Jahr: 2023
• Umfang: 12 S.
• Fussnoten: Online veröffentlicht am 21. September 2022 ; Gesehen am 26.09.2023
• Titel Quelle: Enthalten in: Journal of computational and graphical statistics
• Ort Quelle: Alexandria, Va. : Taylor & Francis Group, 1992
• Jahr Quelle: 2023
• Band/Heft Quelle: 32(2023), 2, Seite 539-550
• ISSN Quelle: 1537-2715
• DOI: doi:10.1080/10618600.2022.2102026
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Acceptance regions
• Sach-SW: Goodness-of-fit test
• Sach-SW: Log-likelihood ratio
• Sach-SW: Pearson’s Chi-square
• Sach-SW: Probability mass statistic
• Sach-SW: R software
• K10plus-PPN: 1860278280

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.