Motivated by applications in text mining and discrete distribution inference,
we investigate the testing for equality of probability mass functions of K
groups of high-dimensional multinomial distributions. A test statistic, which
is shown to have an asymptotic standard normal distribution under the null, is
proposed. The optimal detection boundary is established, and the proposed test
is shown to achieve this optimal detection boundary across the entire parameter
space of interest. The proposed method is demonstrated in simulation studies
and applied to analyze two real-world datasets to examine variation among
consumer reviews of Amazon movies and diversity of statistical paper abstracts