论文标题
RV系数的确切第一瞬间通过不变的正交整合
Exact first moments of the RV coefficient by invariant orthogonal integration
论文作者
论文摘要
RV系数测量了两种多元配置之间的相似性，其显着性测试在过去几十年中吸引了各种建议。我们提出了一种新的方法，即不变的正交整合，允许在零假设下获得RV系数的确切四个矩。它在于沿HAAR测量两种配置的各个方向，并且可以应用于观测值之间具有欧几里得距离的任何多元设置。我们的建议还涵盖了不平等重要性观察的加权设置，在这种情况下，交换性假设（证明通常的置换测试是合理的）。 提出的RV矩表达为在两个配置的加权多维缩放中发生的内核特征值的简单函数。第三和第四刻的表达似乎是原始的。可以通过基本手段获得前三个时刻，但是计算第四刻需要一个更复杂的仪器，即正交组的Weingarten演算。强调了标准内核及其光谱矩的核心作用。
The RV coefficient measures the similarity between two multivariate configurations, and its significance testing has attracted various proposals in the last decades. We present a new approach, the invariant orthogonal integration, permitting to obtain the exact first four moments of the RV coefficient under the null hypothesis. It consists in averaging along the Haar measure the respective orientations of the two configurations, and can be applied to any multivariate setting endowed with Euclidean distances between the observations. Our proposal also covers the weighted setting of observations of unequal importance, where the exchangeability assumption, justifying the usual permutation tests, breaks down. The proposed RV moments express as simple functions of the kernel eigenvalues occurring in the weighted multidimensional scaling of the two configurations. The expressions for the third and fourth moments seem original. The first three moments can be obtained by elementary means, but computing the fourth moment requires a more sophisticated apparatus, the Weingarten calculus for orthogonal groups. The central role of standard kernels and their spectral moments is emphasized.
