Poisson approximation for two scan statistics with rates of convergence

TL;DR

This paper applies Stein's method to derive convergence rates for the tail probabilities of two scan statistics used in detecting local signals in sequences, addressing both ordinary and large deviations.

Contribution

It introduces a novel application of Stein's method to obtain explicit convergence rates for scan statistics' tail probabilities, covering both typical and large deviation regimes.

Findings

Established convergence rates for tail probabilities of scan statistics.

Unified treatment of ordinary and large deviations.

Enhanced understanding of detection thresholds in change-point analysis.

Abstract

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables subject to possible change-points. Our formulation deals simultaneously with ordinary and with large deviations.