论文标题
高维白噪声的基于等级的测试
Rank Based Tests for High Dimensional White Noise
论文作者
论文摘要
高维白噪声测试的发展在统计理论和应用中都很重要，在统计理论和应用中，时间序列的维度可以与时间序列的长度相当或超过时间序列。本文提出了使用基于等级的统计数据来测试高维白噪声的几项无分配测试，这些噪声对重型尾巴很健壮，并且不会对样本分布的有限级订单矩假设进行询问。本文分析了三个基于等级的测试的家族，包括简单的线性等级统计，非分类U统计量和退化U统计量。为这些测试的每个家族建立了渐近的无效分布和速率最佳性。在这些测试中，基于退化的U统计量的测试还可以检测自相关中的非线性和非单调关系。此外，这是等级相关统计的渐近分布的第一个结果，该结果允许在高维数据中横断面依赖性。
The development of high-dimensional white noise test is important in both statistical theories and applications, where the dimension of the time series can be comparable to or exceed the length of the time series. This paper proposes several distribution-free tests using the rank based statistics for testing the high-dimensional white noise, which are robust to the heavy tails and do not quire the finite-order moment assumptions for the sample distributions. Three families of rank based tests are analyzed in this paper, including the simple linear rank statistics, non-degenerate U-statistics and degenerate U-statistics. The asymptotic null distributions and rate optimality are established for each family of these tests. Among these tests, the test based on degenerate U-statistics can also detect the non-linear and non-monotone relationships in the autocorrelations. Moreover, this is the first result on the asymptotic distributions of rank correlation statistics which allowing for the cross-sectional dependence in high dimensional data.
