Inference for Change Point and Post Change Means After a CUSUM Test

This monograph is the first to systematically study the bias of estimators and construction of corrected confidence intervals for change-point and post-change parameters after a change is detected by using a CUSUM procedure. Researchers in change-point problems and sequential analysis, time series and dynamic systems, and statistical quality control will find that the methods and techniques are mostly new and can be extended to more general dynamic models where the structural and distributional parameters are monitored. Practitioners, who are interested in applications to quality control, dynamic systems, financial markets, clinical trials and other areas, will benefit from case studies based on data sets from river flow, accident interval, stock prices, and global warming. Readers with an elementary probability and statistics background and some knowledge of CUSUM procedures will be able to understand most results as the material is relatively self-contained. §The exponential family distribution is used as the basic model that includes changes in mean, variance, and hazard rate as special cases. There are fundamental differences between the sequential sampling plan and fixed sample size. Although the results are given under the CUSUM procedure, the methods and techniques discussed provide new approaches to deal with inference problems after sequential change-point detection, and they also contribute to the theoretical aspects of sequential analysis. Many results are of independent interests and can be used to study random walk related stochastic models. §Yanhong Wu is a visiting lecturer in statistics at the University of the Pacific. Previously, he was a visiting associate professor at the University of Michigan and an assistant professor at the University of Alberta. He has published more than forty research papers on the topics of change-point problem, quality control, mixture models, risk theory, and reliability mathematics. He was the receiver of Pierre-Robillard Award from the Canadian Statistical Society.§From the reviews:§"Overall, I recommend the book to anyone working in the area of sequential analysis." Journal of the American Statistical Association, June 2006