标题： 依赖随机变量和与最大值的渐近独立性及其在高维检验中的应用 显示英文标题

标题： Asymptotic Independence of the Sum and Maximum of Dependent Random Variables with Applications to High-Dimensional Tests

摘要： 对于一组相关的随机变量，在不假设平稳性或强混合性的条件下，我们推导出它们的和与最大值之间的渐近独立性。 然后我们将这一结果应用于高维检验问题，其中我们结合了和型检验和极值型检验，并提出了一个新颖的检验过程，用于高维情况下的单样本均值检验、双样本均值检验和回归系数检验。 基于和与最大值之间的渐近独立性，建立了检验统计量的渐近分布。 模拟研究显示，无论数据是否稀疏，我们提出的检验都表现出良好的性能。 还给出了实际数据的例子，以展示我们提出方法的优势。 显示英文摘要

摘要： For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we combine the sum-type and max-type tests and propose a novel test procedure for the one-sample mean test, the two-sample mean test and the regression coefficient test in high-dimensional setting. Based on the asymptotic independence between sums and maxima, the asymptotic distributions of test statistics are established. Simulation studies show that our proposed tests have good performance regardless of data being sparse or not. Examples on real data are also presented to demonstrate the advantages of our proposed methods.