论文标题
二次形式的渐近独立性和具有高维测试应用的独立随机变量的最大独立性
Asymptotic Independence of the Quadratic form and Maximum of Independent Random Variables with Applications to High-Dimensional Tests
论文作者
论文摘要
本文建立了二次形式和一系列独立随机变量序列之间的渐近独立性。基于这个理论结果，我们发现二次形式和最大形式的渐近关节分布，可以应用于高维测试问题。通过将SUMTYPE测试和最大型测试结合起来，我们提出了Fisher的一样本平均测试和两样本平均测试的组合测试。在这个新颖的一般框架下，现有文献中的一些有力的假设已经放松。已经进行了蒙特卡洛模拟，这表明我们提出的测试对稀疏和密集数据都非常强大。
This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and maximum, which can be applied into the high-dimensional testing problems. By combining the sum-type test and the max-type test, we propose the Fisher's combination tests for the one-sample mean test and two-sample mean test. Under this novel general framework, several strong assumptions in existing literature have been relaxed. Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.
