Third-order asymptotic optimality of the generalized shiryaev-roberts changepoint detection procedures

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 R0 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.