基于不变性的随机过程移动和分段
Moving sum data segmentation for stochastics processes based on invariance
AI总结：
本文基于强不变性原理，利用移动和统计量对一类状态切换多元过程进行数据分割，证明了变点估计量的一致性并推导了极小极大最优定位速率，还给出了局部变化下的极限分布。
摘要：
将数据分割成平稳片段（也称为多变点问题）对于时间序列分析和信号处理中的许多应用非常重要。基于强不变性原理，我们分析了一类使用移动和（MOSUM）统计量的数据分割方法，该方法适用于一类状态切换的多元过程，其中每次切换都会导致漂移的变化。特别地，该框架包括多元部分和、积分扩散和更新过程的数据分割，即使变点之间的距离是次线性的。我们研究了相应变点估计量的渐近行为，证明了一致性，并推导了相应的定位速率，这些速率在各种情况下（包括带漂移的维纳过程中无界数量的变化）都是极小极大最优的。此外，我们推导了局部变化下变点估计量的极限分布——这一结果原则上可用于推导变点的置信区间。
英文摘要：
The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data segmentation methodology using moving sum (MOSUM) statistics for a class of regime-switching multivariate processes where each switch results in a change in the drift. In particular, this framework includes the data segmentation of multivariate partial sum, integrated diffusion and renewal processes even if the distance between change points is sublinear. We study the asymptotic behaviour of the corresponding change point estimators, show consistency and derive the corresponding localisation rates which are minimax optimal in a variety of situations including an unbounded number of changes in Wiener processes with drift. Furthermore, we derive the limit distribution of the change point estimators for local changes - a result that can in principle be used to derive confidence intervals for the change points.
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