Power Analysis of Projection-Pursuit Independence Tests
Power Analysis of Projection-Pursuit Independence Tests
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DOI：
10.5705/ss.202019.0457
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发表时间：
2022
影响因子：
1.4
通讯作者：
Kai Xu;Liping Zhu
中科院分区：
文献类型：
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作者：
Kai Xu;Liping Zhu
文献中已提出三种重要的投影寻踪相关性，即距离相关性、投影相关性以及多元布鲁姆 - 基弗 - 罗森布拉特（BKR）相关性，用于检验任意维度下两个随机向量之间的独立性。在本文中，我们从一致意义上比较了基于这三种投影寻踪相关性构建的独立性检验的渐近功效表现。我们表明，在存在异常值的情况下，投影相关性检验和多元BKR相关性检验仍然具有较高功效，而距离相关性检验可能会丧失功效。我们还分析了这些独立性检验的极小极大最优性。我们证明它们的最小分离率为\(n^{-1}\)阶，其中\(n\)表示样本量，并且就投影相关性、距离相关性和多元BKR相关性而言，这个极小极大最优速率分别是紧致的。
Three important projection-pursuit correlations, namely, distance cor1 relation, projection correlation and the multivariate Blum-Kiefer-Rosenblatt (BKR) 2 correlation, have been proposed in the literature to test independence between 3 two random vectors in arbitrary dimensions. In this paper we compare the asymp4 totic power performance of independence tests built upon these three projection5 pursuit correlations in a uniform sense. We show that, in the presence of outliers, 6 the projection correlation test and the multivariate BKR correlation test are still 7 powerful, whereas the distance correlation test may lose power. We also analyze 8 the minimax optimality of these independence tests. We show that their mini9 mum separation rates are of order n−1, where n stands for the sample size, and 10 this minimax optimal rate is tight in terms of projection correlation, distance 11 correlation and multivariate BKR correlation, respectively. 12