Two-sample test for sparse high-dimensional multinomial distributions

In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical Chi-square test may have some drawbacks in this case since many of cell counts may be zero or may not be large enough. We propose a new test and show its asymptotic normality and the asymptotic power function. Based on the asymptotic power function, we present an application of our result to a neighborhood-type test which has been previously studied, especially for the case of fairly small p values. To compare the proposed test with existing tests, we provide numerical studies including simulations and real data examples.