Truncated sequential change-point detection based on renewal counting processes II

The standard approach in change-point theory is to base the statistical analysis on a sample of fixed size. Alternatively, one observes some random phenomenon sequentially and takes action as soon as one observes some statistically significant deviation from the “normal” behaviour. The present paper is a continuation of Gut and Steinebach [2002. Truncated sequential change-point detection based on renewal counting processes. Scand. J. Statist. 29, 693–719] the main point being that here we look in more detail into the behaviour of the relevant stopping times, in particular the time it takes from the actual change-point until the change is detected, more precisely, we prove asymptotics for stopping times under alternatives.