Preface

The change-point problem has attracted many statistical researchers and practitioners during the last few decades. Here, we only concentrate on the sequential change-point problem. Starting from the Shewhart chart with applications to quality control [see Shewhart (1931)], several monitoring procedures have been developed for a quick detection of change. The three most studied monitoring procedures are the CUSUM procedure [Page (1954)], the EWMA procedure [Roberts (1959)] and the Shiryayev−Roberts procedure [Shiryayev (1963) and Roberts (1966)]. Extensive studies have been conducted on the performances of these monitoring procedures and comparisons in terms of the delay detection time. Lai (1995) made a review on the state of the art on these charts and proposed several possible generalizations in order to detect a change in the case of the unknown post-change parameter case. In particular, a windowlimited version of the generalized likelihood ratio testing procedure studied by Siegmund and Venkatraman (1993) is proposed for a more practical treatment even when the observations are correlated. In this work, our main emphasis is on the inference problem for the changepoint and the post-change parameters after a signal of change is made. More specifically, due to its convenient form and statistical properties, most discussions are concentrated on the CUSUM procedure. Our goal is to provide some quantitative evaluations on the statistical properties of estimators for the change-point and the post-change parameters. It has to be stressed that there have been many studies on the inference problem for the change-point in the fixed sample size case under both parametric models and nonparametric models. The inference problem after sequential detection raises both theoretical and