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