AI 中文总结
本文提出基于边际似然比秩统计量的高维两样本检验框架，通过SUM、MAX及柯西组合统计量检测分布差异，在弱相依下建立渐近理论，并验证了其在模拟与真实数据中的有效性。
AI 中文摘要
我们开发了一个基于秩的高维两样本检验框架，用于检测均值与方差之外的边际分布差异。三种边际似然比统计量分别生成用于检测广泛差异的SUM检验、用于检测集中偏离的MAX检验，以及用于未知信号稀疏性的柯西组合检验。这些程序保留所有合并秩，且对连续边际不施加矩条件。对于样本量不等但可比、且维度随样本总量多项式增长的情形，在弱高斯连接函数依赖下，我们建立了学生化SUM统计量的正态极限和标准化MAX统计量的Gumbel极限。其族内渐近独立性使得组合统计量具有标准柯西极限。积分最大值需要族特定的中心化校正，以适应内部、临界和边界区域。在边际和聚合信号收缩的情形下建立了相合性，其中柯西组合在指定的稀疏和稠密备择类上保留MAX或SUM的相合性。模拟研究考察了位置、尺度和形状变化，包括保持前两阶矩不变的备择情形。对帕金森队列的声学测量和白血病基因表达数据的应用，展示了SUM和MAX聚合的互补优势。
英文摘要
We develop a rank-based framework for high-dimensional two-sample testing that detects marginal distributional differences beyond means and variances. Three marginal likelihood-ratio statistics generate SUM tests for widespread differences, MAX tests for concentrated departures, and Cauchy combinations for unknown signal sparsity. The procedures retain all pooled ranks and impose no moment conditions on continuous margins. For unequal but comparable sample sizes and dimension growing polynomially with their total, we establish normal limits for the studentized SUM statistics and Gumbel limits for the normalized MAX statistics under weak Gaussian-copula dependence. Their within-family asymptotic independence yields standard Cauchy limits for the combinations. The integrated maxima require family-specific centering corrections that accommodate interior, critical, and boundary regimes. Consistency is established under shrinking marginal and aggregate signals, with Cauchy combinations retaining MAX or SUM consistency on specified sparse and dense alternative classes. Simulations examine location, scale, and shape changes, including alternatives preserving the first two moments. Applications to acoustic measurements from a Parkinson's cohort and leukemia gene-expression data illustrate the complementary benefits of SUM and MAX aggregation.
