Detecting changes in the second moment structure of high-dimensional sensor-type data in a K-sample setting

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2020-01-15 DOI:10.1080/07474946.2020.1823192

Nils Mause, A. Steland

引用次数: 2

Abstract

Abstract The K sample problem for high-dimensional vector time series is studied, especially focusing on sensor data streams, in order to analyze the second moment structure and detect changes across samples and/or across variables cumulated sum (CUSUM) statistics of bilinear forms of the sample covariance matrix. In this model, K independent vector time series are observed over a time span which may correspond to K sensors (locations) yielding d-dimensional data as well as K locations where d sensors emit univariate data. Unequal sample sizes are considered as arising when the sampling rate of the sensors differs. We provide large-sample approximations and two related change point statistics, a sum of squares and a pooled variance statistic. The resulting procedures are investigated by simulations and illustrated by analyzing a real data set.

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在K样本设置中检测高维传感器类型数据的二阶矩结构的变化

摘要研究了高维向量时间序列的K样本问题，特别是关注传感器数据流，以分析二阶矩结构，并检测样本协方差矩阵双线性形式的样本间和/或变量间累积和（CUSUM）统计量的变化。在该模型中，在一个时间跨度上观察到K个独立的矢量时间序列，该时间跨度可以对应于产生d维数据的K个传感器（位置）以及d个传感器发射单变量数据的K位置。当传感器的采样率不同时，会出现样本大小不等的情况。我们提供了大样本近似和两个相关的变化点统计，一个平方和和和一个合并方差统计。通过仿真研究了产生的过程，并通过分析真实数据集进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.