We consider two-sample tests for high-dimensional data under two disjoint models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. We provide a general test statistic as a function of a positive-semidefinite matrix. We give sufficient conditions for the test statistic to satisfy a consistency property and to be asymptotically normal. We discuss an optimality of the test statistic under the NSSE model. We also investigate the test statistic under the SSE model by considering strongly spiked eigenstructures and create a new effective test procedure for the SSE model. Finally, we discuss the performance of the classifiers numerically.

中文翻译：

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高维强尖峰特征值模型的两样本检验

我们考虑在两个不相交的模型下对高维数据进行双样本检验：强尖峰特征值 (SSE) 模型和非 SSE (NSSE) 模型。我们提供了作为正半定矩阵函数的一般检验统计量。我们给出了检验统计量满足一致性属性和渐近正态的充分条件。我们讨论了 NSSE 模型下检验统计量的最优性。我们还通过考虑强尖峰特征结构来研究 SSE 模型下的测试统计量，并为 SSE 模型创建新的有效测试程序。最后，我们数值讨论了分类器的性能。