2019/06/08 by Cheng–Der Fuh, Fuh, Cheng-Der · 1 citation
Decision Sciences · #Advanced Statistical Process Monitoring #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1906.03416
openalex publication_date 2019/06/08 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
This paper investigates change point detection in state space models, in\nwhich the pre-change distribution f\θ0 is given, while the poster\ndistribution f\θ after change is unknown. The problem is to raise an\nalarm as soon as possible after the distribution changes from f\θ0 to\nf\θ, under a restriction on the false alarms. We investigate\ntheoretical properties of a weighted Shiryayev-Roberts-Pollak (SRP) change\npoint detection rule in state space models. By making use of a Markov chain\nrepresentation for the likelihood function, exponential embedding of the\ninduced Markovian transition operator, nonlinear Markov renewal theory, and\nsequential hypothesis testing theory for Markov random walks, we show that the\nweighted SRP procedure is second-order asymptotically optimal. To this end, we\nderive an asymptotic approximation for the expected stopping time of such a\nstopping scheme when the change time \ω = 1. To illustrate our method we\napply the results to two types of state space models: general state Markov\nchains and linear state space models.\n