A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data
A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data
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DOI：
10.1080/01621459.2013.849605
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发表时间：
2014-03-01
影响因子：
3.7
通讯作者：
James, Nicholas A.
中科院分区：
文献类型：
--
作者：
Matteson, David S.;James, Nicholas A.
变点分析在许多领域都有应用。一般问题涉及对一组按时间排序的观测值的分布变化的推断。顺序检测是一种在线版本，其中新数据不断到达并进行自适应分析。我们关注的是相关但不同的离线版本，在该版本中，对整个序列进行了追溯分析。对于任意维的一组多元观测，我们考虑了变点个数及其出现位置的非参数估计。我们不做任何关于分布变化的性质的假设，或者对于某个α-epsilon(0，2)，除了存在α的绝对矩之外的任何分布假设。估计是基于层次聚类的，我们提出了分裂算法和凝聚算法。结果表明，在标准的正则性假设下，分裂方法能够对变化点的数量和位置提供一致的估计。我们在仿真研究中将所提出的方法与已有的方法进行了比较。应用聚类分析的方法来评估业绩，并允许对地点估计进行简单的比较，即使估计的数字不同。我们总结了在遗传学、金融学和时空分析中的应用。这篇文章的补充材料可以在网上找到。
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data are continually arriving and are analyzed adaptively. We are concerned with the related, but distinct, offline version, in which retrospective analysis of an entire sequence is performed. For a set of multivariate observations of arbitrary dimension, we consider nonparametric estimation of both the number of change points and the positions at which they occur. We do not make any assumptions regarding the nature of the change in distribution or any distribution assumptions beyond the existence of the alpha th absolute moment, for some alpha epsilon (0, 2). Estimation is based on hierarchical clustering and we propose both divisive and agglomerative algorithms. The divisive method is shown to provide consistent estimates of both the number and the location of change points under standard regularity assumptions. We compare the proposed approach with competing methods in a simulation study. Methods from cluster analysis are applied to assess performance and to allow simple comparisons of location estimates, even when the estimated number differs. We conclude with applications in genetics, finance, and spatio-temporal analysis. Supplementary materials for this article are available online.