On Optimality Properties of the Shiryaev-Roberts Procedure

TL;DR

This paper explores the optimality properties of the Shiryaev-Roberts procedure in changepoint detection, demonstrating its minimax optimality and additional optimality features under specific conditions.

Contribution

The paper reveals new optimality properties of the Shiryaev-Roberts procedure beyond its known asymptotic minimaxity in changepoint detection.

Findings

Shiryaev-Roberts is asymptotically minimax for false alarm constraints.

The procedure exhibits additional optimality properties under certain conditions.

Theoretical analysis confirms robustness of the Shiryaev-Roberts method.

Abstract

We consider the simple changepoint problem setting, where observations are independent, iid pre-change and iid post-change, with known pre- and post-change distributions. The Shiryaev-Roberts detection procedure is known to be asymptotically minimax in the sense of minimizing maximal expected detection delay subject to a bound on the average run length to false alarm, as the latter goes to infinity. Here we present other optimality properties of the Shiryaev-Roberts procedure.