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 $R_0=0$ (the original Shiryaev--Roberts procedure), at $R_0=r$ for fixed $r>0$, and at $R_0$ that has the 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 third-order asymptotically optimal.

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