标题： 自相关数据变化检测的累积和图与Shiryaev-Roberts程序的性能比较分析 显示英文标题

标题： Comparative Performance Analysis of the Cumulative Sum Chart and the Shiryaev-Roberts Procedure for Detecting Changes in Autocorrelated Data

摘要： 我们研究了快速变化点检测的问题，其中观测值构成一个一阶自回归（AR）过程，由时间上独立的标准高斯噪声驱动。 可能发生变化的是AR(1)过程的漂移（$\mu$）以及其相关系数（$\lambda$），两者均为已知。 这种变化是突然且持久的，并且已知变化幅度，整个过程中为 $\vert\lambda\vert<1$。 针对此场景，我们对流行的累积和（CUSUM）图及其不太为人所知但值得重视的竞争者——Shiryaev-Roberts（SR）程序进行了比较性能分析。 具体而言，性能通过Pollak的延迟检测（SADD）的条件平均延迟来衡量，该延迟受平均运行长度（ARL）到误报的预设水平约束。 特别注意每个程序的SADD和ARL对变化前后的$\lambda$值的敏感性。 通过蒙特卡洛模拟获得的积分更新方程的解来研究性能。 这些模拟旨在以无偏且渐近强一致的方式估计所需的性能度量，并在规定比例接近范围内完成（同样渐近）。 我们的广泛数值研究表明，即使CUSUM图略优于SR程序，无论模型参数如何，CUSUM图和SR程序都具有渐近二阶最优性。 此外，还建立了最坏情况下的变化后相关参数的存在性，对应于给定误报的平均运行长度下的最差可探测性。 据我们所知，这是首次对SR程序在自相关数据上的性能进行研究。 显示英文摘要

摘要： We consider the problem of quickest change-point detection where the observations form a first-order autoregressive (AR) process driven by temporally independent standard Gaussian noise. Subject to possible change are both the drift of the AR(1) process ($\mu$) as well as its correlation coefficient ($\lambda$), both known. The change is abrupt and persistent, and is of known magnitude, with $\vert\lambda\vert<1$ throughout. For this scenario, we carry out a comparative performance analysis of the popular Cumulative Sum (CUSUM) chart and its less well-known but worthy competitor -- the Shiryaev-Roberts (SR) procedure. Specifically, the performance is measured through Pollak's Supremum (conditional) Average Delay to Detection (SADD) constrained to a pre-specified level of the Average Run Length (ARL) to false alarm. Particular attention is drawn to the sensitivity of each procedure's SADD and ARL with respect to the value of $\lambda$ before and after the change. The performance is studied through the solution of the respective integral renewal equations obtained via Monte Carlo simulations. The simulations are designed to estimate the sought performance metrics in an unbiased and asymptotically strongly consistent manner, and to within a prescribed proportional closeness (also asymptotically). Our extensive numerical studies suggest that both the CUSUM chart and the SR procedure are asymptotically second-order optimal, even though the CUSUM chart is found to be slightly better than the SR procedure, irrespective of the model parameters. Moreover, the existence of a worst-case post-change correlation parameter corresponding to the poorest detectability of the change for a given ARL to false alarm is established as well. To the best of our knowledge, this is the first time the performance of the SR procedure is studied for autocorrelated data.