Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures

Details Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures

2010-05-07

arxiv.org/abs/1005.1129v3

Mathematics

Statistics Theory

28 pages, 4 figures, Theory of Probability and Its Applications (to appear)

Scientific paper

Several variations of the Shiryaev-Roberts detection procedure in the context of the simple changepoint problem are considered: starting the procedure at $R_0=0$ (the original Shiryaev-Roberts procedure), at $R_0=r$ for fixed $r>0$, and at $R_0$ that has a quasi-stationary distribution. Comparisons of operating characteristics are made. The differences fade as the average run length to false alarm tends to infinity. It is shown that the Shiryaev-Roberts procedures that start either from a specially designed point $r$ or from the random "quasi-stationary" point are order-3 asymptotically optimal.

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