Optimal sequential detection by sparsity likelihood

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computational Statistics & Data Analysis Pub Date : 2024-11-17 DOI:10.1016/j.csda.2024.108089

Jingyan Huang, Hock Peng Chan

引用次数: 0

Abstract

We propose here a sparsity likelihood stopping rule to detect change-points when there are multiple data streams. It is optimal in the sense of minimizing, asymptotically, the detection delay when the change-points is present in only a small fraction of the data streams. This optimality holds at all levels of change-point sparsity. A key contribution of this paper is that we show optimality when there is extreme sparsity. Extreme sparsity refers to the number of data streams with change-points increasing very slowly as the number of data streams goes to infinity. The theoretical results are backed by a numerical study that shows the sparsity likelihood stopping rule performing well at all levels of sparsity. Applications of the stopping rule on non-normal models are also illustrated here.

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利用稀疏似然法优化顺序检测

在此，我们提出了一种稀疏似然停止规则，用于在存在多个数据流时检测变化点。当变化点只出现在一小部分数据流中时，该规则在渐近最小化检测延迟的意义上是最优的。这种最优性在所有变化点稀疏程度上都成立。本文的一个重要贡献是，我们展示了极端稀疏性时的最优性。所谓极端稀疏性，是指当数据流的数量达到无穷大时，数据流中变化点的数量会非常缓慢地增加。理论结果得到了数值研究的支持，数值研究显示稀疏性似然停止规则在所有稀疏性水平下都表现良好。这里还说明了停止规则在非正态模型中的应用。

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

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]

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