论文标题
使用U统计数据的高维数据中的更改点检测
Change point detection in high dimensional data with U-statistics
论文作者
论文摘要
我们考虑在一系列高维数据中检测分布变化的问题。我们的方法结合了两个单独的统计数据，这些统计数据是$ L_P $规范的，其行为在$ H_0 $下相似，但在$ H_A $下可能有所不同，从而导致测试程序具有针对各种替代方案的灵活性。在较弱且依赖依赖的坐标为$ \ min \ {n，d \} \ to \ infty $的情况下，我们分别建立了我们提出的测试统计数据的渐近分布，其中$ n $表示样本大小，而$ d $是尺寸，并在高点上建立一致性和估算程序的一致性和估算程序，在一点点又一次的设置下。单个和多个变更点方案中的计算研究表明，我们的方法可以优于文献中某些替代方案的其他非参数方法。我们说明了我们对美国州长提及的Twitter数据的申请。
We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from $L_p$ norms whose behavior is similar under $H_0$ but potentially different under $H_A$, leading to a testing procedure that that is flexible against a variety of alternatives. We establish the asymptotic distribution of our proposed test statistics separately in cases of weakly dependent and strongly dependent coordinates as $\min\{N,d\}\to\infty$, where $N$ denotes sample size and $d$ is the dimension, and establish consistency of testing and estimation procedures in high dimensions under one-change alternative settings. Computational studies in single and multiple change point scenarios demonstrate our method can outperform other nonparametric approaches in the literature for certain alternatives in high dimensions. We illustrate our approach though an application to Twitter data concerning the mentions of U.S. Governors.
