Asymptotic Near-Minimaxity of the Randomized Shiryaev-Roberts-Pollak Change-Point Detection Procedure in Continuous Time

TL;DR

This paper proves that the randomized Shiryaev-Roberts-Pollak procedure is asymptotically nearly minimax-optimal for continuous-time change-point detection, providing explicit performance analysis and improving previous results.

Contribution

It establishes asymptotic near-minimaxity of the procedure with explicit performance formulas, advancing the theoretical understanding of optimal change detection methods.

Findings

Proves asymptotic near-minimaxity of the procedure.

Provides explicit analytical performance characteristics.

Achieves a one-order improvement over previous results.

Abstract

For the classical continuous-time quickest change-point detection problem it is shown that the randomized Shiryaev-Roberts-Pollak procedure is asymptotically nearly minimax-optimal (in the sense of Pollak 1985) in the class of randomized procedures with vanishingly small false alarm risk. The proof is explicit in that all of the relevant performance characteristics are found analytically and in a closed form. The rate of convergence to the (unknown) optimum is elucidated as well. The obtained optimality result is a one-order improvement of that previously obtained by Burnaev et al. (2009) for the very same problem.