Power of the MOSUM test for online detection of a transient change in mean

Online change-point detection for a transient change

“…For the MOSUM procedure given in (3.11), the quantity (3.34) was the focus of study in [24] and built on the continuous time results of [26]. For T = l + L, the quantity (3.34) is equivalent to:…”

“…Formally, we require ν → ∞ in (3.35). This is to ensure that the sequence of moving sums {S n,L } n reaches the stationary behaviour under the null hypothesis and given that we have not crossed the threshold H. However, as discussed [24,26], this stationary regime is reached very quickly and in all approximations it is enough to only require ν ≥ 2L. The reasoning behind the choice T = l + L is as follows.…”

“…where P S (H, A, L) = P ξ (h, A, L). To approximate P ξ (h, A, L), the approach taken in [24] was similar to the approach take to approximate ARL. The approach is as follows.…”

“…The complexity of computation of the diffusion approximation P(h, A) and its discrete-time corrected version depends on the choice of L in comparison to l. Here, we will only consider the scenario of λ = l/L = 1 which corresponds to the case of l known at the MOSUM construction stage. The two other cases of λ > 1 and λ < 1 are studied in [24].…”

“…The case of finite l, and hence when a change occurs it does so temporarily, has seen considerable attention in the past, see [16,17,18,19,20,21,22,23]. More re-cently it has been the focus of attention in the papers of [24,25,26]. Examples of areas where detecting a transient change in distributions is extremely important can be found in radar and sonar [27,28,29], nondestructive testing [30], and medicine [31].…”