High dimensional efficiency with applications to change point tests
High dimensional efficiency with applications to change point tests
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DOI：
10.1214/18-ejs1442
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发表时间：
2018
影响因子：
1.1
通讯作者：
J. Aston;C. Kirch
中科院分区：
文献类型：
--
作者：
J. Aston;C. Kirch
：本文严格介绍了高维效率的渐近概念，该概念可以量化高维多变量设置中不同统计的检测能力，从而可以比较不同的高尺寸方法与不同的无效行为。 。研究，因为在许多高维情况下，小组中多元观察的全部依赖性（共同变化）通常是在计算上或什至是可行的。令人惊讶的小样本的理论（渐近）发现是由这种概念的发展，但绝不限于高维变化点测试。样本功率。
: This paper rigourously introduces the asymptotic concept of high dimensional efficiency which quantifies the detection power of different statistics in high dimensional multivariate settings. It allows for comparisons of different high dimensional methods with different null asymptotics and even different asymptotic behavior such as extremal-type asymptotics. The concept will be used to understand the power behavior of different test statistics as the performance will greatly depend on the assumptions made, such as sparseness or denseness of the signal. The effect of misspecification of the covariance on the power of the tests is also investigated, because in many high dimensional situations estimation of the full dependency (co-variance) between the multivariate observations in the panel is often either computationally or even theoretically infeasible. The theoretic quantifica-tion by the theory is accompanied by simulation results which confirm the theoretic (asymptotic) findings for surprisingly small samples. The development of this concept was motivated by, but is by no means limited to, high-dimensional change point tests. It is shown that the concept of high dimensional efficiency is indeed suitable to describe small sample power. MSC 2010 subject classifications: 62F05, 62M10, 62G10