Wang Peiyao, Ning Wei
Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN, USA.
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, USA.
J Appl Stat. 2024 Jan 23;51(13):2558-2591. doi: 10.1080/02664763.2024.2307532. eCollection 2024.
Sequential change-point analysis, which identifies a change of probability distribution in an infinite sequence of random observations, has important applications in many fields. A good method should detect a change point as soon as possible, and keep a low amount of false alarms. As one of the most popular methods, Shiryaev-Roberts (SR) procedure holds many optimalities. However, its implementation requires the pre-change and post-change distributions to be known, which is not achievable in practice. In this paper, we construct a nonparametric version of the SR procedure by embedding different versions of empirical likelihood, assuming two training samples, before and after change, are available for parameter estimations. Simulations are conducted to compare the performance of the proposed method with existing methods. The results show that when the underlying distribution is unknown, and training sample sizes are small, the proposed modified procedure shows advantage by giving a smaller delay of detection.
序贯变点分析用于识别无限随机观测序列中概率分布的变化，在许多领域都有重要应用。一个好的方法应该尽快检测到变点，并保持较低的误报率。作为最流行的方法之一， Shiryaev-Roberts（SR）程序具有许多最优性。然而，它的实施需要知道变化前和变化后的分布，这在实际中是无法实现的。在本文中，我们通过嵌入不同版本的经验似然来构建SR程序的非参数版本，假设可以获得变化前后的两个训练样本用于参数估计。进行了模拟以比较所提出的方法与现有方法的性能。结果表明，当基础分布未知且训练样本量较小时，所提出的改进程序通过给出较小的检测延迟而显示出优势。
