泊松点过程的多变点检测
Multiple change-point detection for Poisson point processes
AI总结：
针对非齐次或标记泊松过程数据，提出基于最小对比度估计的离线多变点检测方法，通过交叉验证选择变点数量，并推广至自激励过程。
摘要：
变点检测的目标是识别时间序列数据中的行为转变。本文关注数据源自非齐次泊松过程或标记泊松过程的情形。我们提出了一种使用最小对比度估计来检测多个离线变点的方法。具体来说，我们解决了在给定离散观测的情况下如何管理过程的连续性质。此外，我们通过交叉验证程序选择适当的变点数量，该程序鉴于泊松过程的特性特别有效。最后，我们展示了如何将此方法用于强度变化的自激励过程。通过模拟和真实数据集的实验，我们展示了所提出方法的优势，该方法已在R包中实现。
英文摘要：
The aim of change-point detection is to identify behavioral shifts within time series data. This article focuses on scenarios where the data is derived from an inhomogeneous Poisson process or a marked Poisson process. We present a methodology for detecting multiple offline change-points using a minimum contrast estimator. Specifically, we address how to manage the continuous nature of the process given the available discrete observations. Additionally, we select the appropriate number of changes via a cross-validation procedure which is particularly effective given the characteristics of the Poisson process. Lastly, we show how to use this methodology for self-exciting processes with changes in the intensity. Through experiments, with both simulated and real datasets, we showcase the advantages of the proposed method, which has been implemented in the R package.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
