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On some consistent tests of mutual independence among several random vectors of arbitrary dimensions

机译：关于任意尺寸的几种随机载体中相互独立的一致测试

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摘要

Testing for mutual independence among several random vectors is a challenging problem, and in recent years, it has gained significant attention in statistics and machine learning literature. Most of the existing tests of independence deal with only two random vectors, and they do not have straightforward generalizations for testing mutual independence among more than two random vectors of arbitrary dimensions. On the other hand, there are various tests for mutual independence among several random variables, but these univariate tests do not have natural multivariate extensions. In this article, we propose two general recipes, one based on inter-point distances and the other based on linear projections, for multivariate extensions of these univariate tests. Under appropriate regularity conditions, these resulting tests turn out to be consistent whenever we have consistency for the corresponding univariate tests. We carry out extensive numerical studies to compare the empirical performance of these proposed methods with the state-of-the-art methods.
机译：几种随机载体之间的相互独立性测试是一个具有挑战性的问题，近年来，它在统计和机器学习文学中取得了重大关注。只有两个随机载体的独立性统一测试的大多数，并且它们没有直接的概括，用于在多个任意尺寸的两个随机载体之间测试相互独立性的概括。另一方面，几种随机变量之间的相互独立性有各种测试，但这些单变量测试没有自然多变量扩展。在本文中，我们提出了两个一般的食谱，一个基于点的点距离，基于线性投影，用于这些单变量测试的多变量扩展。在适当的规则条件下，每当我们对相应的单变量测试的一致性保持一致时，这些结果的测试结果是一致的。我们开展了广泛的数值研究，以比较这些提出的方法的实证性能与最先进的方法。

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