2014/08/29 by Wenyu Du, Du, Wenyu, Grigory Sokolov +3
Decision Sciences · Mathematics · #60G40 #62C20 #62L10 #62L15 #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1408.6937
openalex publication_date 2014/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is found through direct solution of the respective integral (renewal) equation, and is a general result in that the GSR procedure's headstart is not restricted to a bounded range, nor is there a "ceiling" value for the detection threshold. Apart from the theoretical significance (in change-point detection, exact closed-form performance formulae are typically either difficult or impossible to get, especially for the GSR procedure), the obtained formula is also useful to a practitioner: in cases of practical interest, the formula is a function linear in both the detection threshold and the headstart, and, therefore, the ARL to false alarm of the GSR procedure can be easily computed.