V. I. Lotov, A. S. Tarasenko, “Study of characteristics of the CUSUM procedure in a change point problem”, Sib. Èlektron. Mat. Izv., 2023, Volume 20, Issue 2,Pages <nobr>987

Probability theory and mathematical statistics

Study of characteristics of the CUSUM procedure in a change point problem

V. I. Lotov, A. S. Tarasenko

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We study properties of the CUSUM procedure in a change point problem. This procedure proposes an algorithm for the fastest detecting change in the distribution of observations. We obtain estimates in the form of inequalities for the average delay time in reacting to a change in distribution and for the average time to a false alarm.

Keywords: random walk with delay at origin, CUSUM procedure, change point problem, probabilistic inequalities.

UDC: 519.21

MSC: 60G50

Received June 26, 2023, published November 12, 2023

DOI: doi.org/10.33048/semi.2023.20.060