  As a fundamental concept in information theory, mutual information ($MI$) has
been commonly applied to quantify association between random vectors. Most
existing nonparametric estimators of $MI$ have unstable statistical performance
since they involve parameter tuning. We develop a consistent and powerful
estimator, called fastMI, that does not incur any parameter tuning. Based on a
copula formulation, fastMI estimates $MI$ by leveraging Fast Fourier
transform-based estimation of the underlying density. Extensive simulation
studies reveal that fastMI outperforms state-of-the-art estimators with
improved estimation accuracy and reduced run time for large data sets. fastMI
provides a powerful test for independence that exhibits satisfactory type I
error control. Anticipating that it will be a powerful tool in estimating
mutual information in a broad range of data, we develop an R package fastMI for
broader dissemination.
