Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures
Abstract
Several variations of the Shiryaev-Roberts detection procedure in the context of the simple changepoint problem are considered: starting the procedure at R0=0 (the original Shiryaev-Roberts procedure), at R0=r for fixed r>0, and at R0 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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