A normal test for independence via generalized mutual information

Abstract

Testing hypothesis of independence between two random elements on a joint alphabet is an important exercise in statistics. Pearson’s chi-squared test is effective for dense contingency tables. General statistical tools are lacking when the contingency tables are non-ordinal and sparse. This article proposes a test based on generalized mutual information, with two main advantages: (1) the test statistic is asymptotically normal under the independence hypothesis (provided the marginals are not uniformly distributed), consequently it does not require the knowledge of the row and column sizes of the contingency table, and (2) the test is consistent and therefore it detects any dependence structure in the general alternative space given a sufficiently large sample. Simulation studies show that the proposed test converges faster than Pearson’s chi-squared test when the contingency table is sparse.