论文标题
总和的渐近独立性和根据高维测试应用的依赖随机变量的最大独立性
Asymptotic Independence of the Sum and Maximum of Dependent Random Variables with Applications to High-Dimensional Tests
论文作者
论文摘要
对于一组依赖性随机变量，没有静止或强烈的混合假设，我们得出了其总和和最大值之间的渐近独立性。然后，我们将此结果应用于高维测试问题，其中我们结合了汇总类型和最大型测试，并提出了一种新型的测试程序，用于一样本平均测试，两样本平均测试以及在高维环境中的回归系数测试。基于总和与最大值之间的渐近独立性，建立了测试统计的渐近分布。仿真研究表明，无论数据稀疏，我们提出的测试的性能良好。还提供了有关真实数据的示例，以证明我们提出的方法的优势。
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.
