Nonparametric independence testing via mutual information
This provides a method for statisticians and data scientists to perform independence testing in multivariate settings, though it is incremental as it builds on existing entropy estimation techniques.
The authors tackled the problem of testing independence between two multivariate random vectors by proposing MINT, a nonparametric test based on mutual information estimation using nearest neighbor entropy estimators, which guarantees nominal size and shows power in simulations and real data.
We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently-developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values, which may be obtained from simulation (in the case where one marginal is known) or resampling, guarantee that the test has nominal size, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide a new goodness-of-fit tests of normal linear models based on assessing the independence of our vector of covariates and an appropriately-defined notion of an error vector. The theory is supported by numerical studies on both simulated and real data.