论文标题
测试高维白噪声
Testing for high-dimensional white noise
论文作者
论文摘要
多维白噪声的测试是统计推断的重要主题。在高维情况下，此类测试成为一个正等待解决的开放问题，尤其是当时间序列的尺寸与样本量相当甚至更大时。为了检测出高度白噪声的任意出发形式，已经开发了一些测试。其中一些测试基于最大型统计数据，而其他测试基于汇总类型。尽管取得了进展，但仍在等待解决的紧急问题：这些测试都不适合串行相关结构的稀疏性。在此激励的情况下，我们根据建立的渐近独立性，通过将最大型和汇总统计数据结合起来，提出了Fisher的组合测试。该组合测试可以使串行相关结构的稀疏性实现鲁棒性，并结合两种测试的优势。通过广泛的数值结果和经验分析，我们证明了拟议测试比某些现有测试的优势。
Testing for multi-dimensional white noise is an important subject in statistical inference. Such test in the high-dimensional case becomes an open problem waiting to be solved, especially when the dimension of a time series is comparable to or even greater than the sample size. To detect an arbitrary form of departure from high-dimensional white noise, a few tests have been developed. Some of these tests are based on max-type statistics, while others are based on sum-type ones. Despite the progress, an urgent issue awaits to be resolved: none of these tests is robust to the sparsity of the serial correlation structure. Motivated by this, we propose a Fisher's combination test by combining the max-type and the sum-type statistics, based on the established asymptotically independence between them. This combination test can achieve robustness to the sparsity of the serial correlation structure,and combine the advantages of the two types of tests. We demonstrate the advantages of the proposed test over some existing tests through extensive numerical results and an empirical analysis.
