Nonparametric two‐sample problems are extremely important for applications in different applied disciplines. We define a general MI based on the φ divergences and use its estimate to propose a new general class of nonparametric two sample tests for continuous distributions. We derive the asymptotic distribution of the estimates of φ‐divergence‐based MI (φDMI) under the assumption of independence in the hybrid setup of one binary and one continuous random variables. Additionally, for finite sample cases, we describe an algorithm for obtaining the bootstrap‐based critical value of our proposed two‐sample test based on the estimated φDMI. We demonstrate through extensive simulations that the proposed class of tests work exceptionally well in many situations and can detect differences where other two‐sample tests fail. Finally, we analyze an application of our proposed tests to assess a solution to information leakage in e‐passport data.

中文翻译：

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使用基于一般φ散度的互信息的非参数两样本检验

非参数两样本问题对于不同应用学科中的应用极为重要。我们基于φ散度定义一个通用的MI，并使用其估计值为连续分布的非参数两个样本检验提出一个新的通用类别。我们得出的估计值的渐近分布φ -divergence基于-MI（φ独立性的一个二进制和一个连续随机变量的混合设置的假设下DMI）。此外，对于有限样本情况，我们描述了一种基于估计的φ来获得拟议的两次样本测试的基于引导的临界值的算法DMI。通过广泛的仿真，我们证明了所提出的测试类别在许多情况下都表现出色，并且可以检测其他两个样本测试失败的差异。最后，我们分析了我们提出的测试的应用，以评估解决电子护照数据中信息泄漏的解决方案。