标题： 关于在后变化分布参数误设情况下Shiryaev-Roberts过程对快速变化点检测的鲁棒性 显示英文标题

标题： On Robustness of the Shiryaev-Roberts Procedure for Quickest Change-Point Detection under Parameter Misspecification in the Post-Change Distribution

摘要： 快速变化点检测问题的核心是在一系列依次进行的观测中检测统计行为的变化，并以最优的检测速度与“假阳性”风险之间的平衡方式来完成这一检测。 当最优性被理解为广义贝叶斯意义上的最优性，或者如Shiryaev的多周期设置中所定义时，所谓的Shiryaev-Roberts（SR）检测过程已被证明是“所能做的最好方法”，但前提是观测值的变前和变后分布都完全指定。 我们考虑一个更现实的设置，即变后分布仅已知到一个参数，因此该参数可能被“错误指定”。 感兴趣的问题是，相对于变后分布参数的可能错误指定，这种原本“最好”的SR过程的敏感性（或鲁棒性）如何。 为了回答这个问题，我们提供了一个案例研究，在特定的高斯场景中，我们允许SR过程在变后分布参数方面“调谐不当”，并数值评估这种“调谐不当”对SR过程提供的Shiryaev（多周期）平稳平均检测延迟的影响。 研究中获得的SR过程的全面定量鲁棒性表征可以用于开发相应的理论，并为SR过程的实际设计提供合理依据。 研究的整体定性结论是预期的：对于对比度较小（较大）的变化以及较低（较高）的误报风险水平，SR过程的鲁棒性较差（较好）。 显示英文摘要

摘要： The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-vs.-"false-positive"-risk manner. When optimality is understood either in the generalized Bayesian sense or as defined in Shiryaev's multi-cyclic setup, the so-called Shiryaev-Roberts (SR) detection procedure is known to be the "best one can do", provided, however, that the observations' pre- and post-change distributions are both fully specified. We consider a more realistic setup, viz. one where the post-change distribution is assumed known only up to a parameter, so that the latter may be "misspecified". The question of interest is the sensitivity (or robustness) of the otherwise "best" SR procedure with respect to a possible misspecification of the post-change distribution parameter. To answer this question, we provide a case study where, in a specific Gaussian scenario, we allow the SR procedure to be "out of tune" in the way of the post-change distribution parameter, and numerically assess the effect of the "mistuning" on Shiryaev's (multi-cyclic) Stationary Average Detection Delay delivered by the SR procedure. The comprehensive quantitative robustness characterization of the SR procedure obtained in the study can be used to develop the respective theory as well as to provide a rational for practical design of the SR procedure. The overall qualitative conclusion of the study is an expected one: the SR procedure is less (more) robust for less (more) contrast changes and for lower (higher) levels of the false alarm risk.