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

TL;DR

This paper analyzes various Shiryaev-Roberts change detection procedures, demonstrating that those starting from specific points or distributions achieve third-order asymptotic optimality as false alarm constraints grow large.

Contribution

It establishes the third-order asymptotic optimality of generalized Shiryaev-Roberts procedures starting from particular initial conditions.

Findings

Procedures starting at a fixed point r are asymptotically optimal.

Procedures starting from a quasi-stationary distribution are also asymptotically optimal.

Differences between procedures diminish as false alarm rate increases.

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 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.