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arXiv · 2008.12682

A Simple Algorithm for Exact Multinomial Tests

Johannes Resin
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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.

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BibTeXRIS

Johannes Resin. 2020-08-28. A Simple Algorithm for Exact Multinomial Tests. https://doi.org/10.1080/10618600.2022.2102026

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