论文标题
通过广义共同信息进行独立的正常测试
A Normal Test for Independence via Generalized Mutual Information
论文作者
论文摘要
在联合字母上两个随机元素之间的独立性测试假设是统计中的基本练习。 Pearson的卡方测试是对应变表相对较小的这种情况的有效测试。当应变数据表大或稀疏时，缺乏一般统计工具。在本文中得出并提出了基于广义相互信息的测试。新测试具有两种所需的理论属性。首先，在独立性假设下，测试统计量渐近地正常。因此，它不需要偶性表的行和列大小的知识。其次，该测试是一致的，因此它将在给定足够大的样本中检测一般替代空间中的任何形式的依赖性结构。此外，模拟研究表明，当偶性表较大或稀疏时，所提出的测试比Pearson的卡方检验更快。
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small. General statistical tools are lacking when the contingency data tables are large or sparse. A test based on generalized mutual information is derived and proposed in this article. The new test has two desired theoretical properties. First, the test statistic is asymptotically normal under the hypothesis of independence; consequently it does not require the knowledge of the row and column sizes of the contingency table. Second, the test is consistent and therefore it would detect any form of dependence structure in the general alternative space given a sufficiently large sample. In addition, simulation studies show that the proposed test converges faster than Pearson's chi-squared test when the contingency table is large or sparse.
