A two-step sequential procedure for detecting an epidemic change (Q2463684)

The authors consider a sequence of independent r.v.s \(X_i\) with an epidemic change of the distribution, i.e., for some \(k_1<k_2\) the CDF of \(X_i\) is \(F(\cdot)\) as \(i\leq k_1\) or \(i>k_2\) and is \(F(\cdot-\Delta)\) for \(k_1<i\leq k_2\). The change points \(k_1\) and \(k_2\) are detected sequentially. A two-step procedure is proposed for the detection based on the standardized increments of the renewal counting process constructed by \(X_i\). The critical values of this procedure are derived via a strong invariance principle.