As a fundamental concept in information theory, mutual information ($MI$) has been commonly applied to quantify the 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 \texttt{fastMI}, that does not incur any parameter tuning. Based on a copula formulation, \texttt{fastMI} estimates $MI$ by leveraging Fast Fourier transform-based estimation of the underlying density. Extensive simulation studies reveal that \texttt{fastMI} outperforms state-of-the-art estimators with improved estimation accuracy and reduced run time for large data sets. \texttt{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 \texttt{fastMI} for broader dissemination.

翻译：作为信息论中的基本概念，互信息（$MI$）已被广泛应用于量化随机向量之间的关联性。现有大多数非参数$MI$估计器因涉及参数调优而表现出不稳定的统计性能。我们开发了一致且高效的估计器\texttt{fastMI}，该估计器无需任何参数调优。基于copula形式，\texttt{fastMI}通过利用基于快速傅里叶变换的底层密度估计来计算$MI$。大量模拟研究表明，\texttt{fastMI}在提高估计精度的同时降低了大型数据集的运行时间，性能优于现有最优估计器。\texttt{fastMI}为独立性检验提供了强有力的工具，并展现出令人满意的第一类错误控制率。鉴于其有望成为广泛数据类型中互信息估计的强大工具，我们开发了R包\texttt{fastMI}以促进其更广泛的应用。