A simple algorithm for exact multinomial tests
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 te...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2023
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| In: |
Journal of computational and graphical statistics
Year: 2023, Volume: 32, Issue: 2, Pages: 539-550 |
| ISSN: | 1537-2715 |
| DOI: | 10.1080/10618600.2022.2102026 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1080/10618600.2022.2102026
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| Author Notes: | Johannes Resin |
| Summary: | 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. |
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| Item Description: | Online veröffentlicht am 21. September 2022 Gesehen am 26.09.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1537-2715 |
| DOI: | 10.1080/10618600.2022.2102026 |