Abstract: Change-point problem primarly arose from the process of quality control in which one concerns about the outputs of a production line and wishes to find any departure from an acceptable standard of the product. The problem of abrupt changed is often encountered in various experimental and mathematical sciences. From a statistical point of view, we wish to infer (detect) whether there is a statistically significant change-point in a sequence of chronologically ordered date. In the case that there is a statistically significant change-point, we also will locate (estimate) the change-point.
In particular, the testing and estimation of multiple covariance change point for a sequence of m-dimensional (m>1) Gaussian random vectors by using Schwarz information criterion (SIC) have been studied. We will estimate the number of change points as well as their locations. The unbiased SIC is also obtained. Then asymptotic null distribution of the test statistic is derived. The result is applied to the weekly prices of Exxon and General Dynamics stocks (m=2) from 1990 to 1991, and changed are successfully detected.

Brief Biography of the Speaker:
Arjun K. Gupta is Distinguished University Professor and former Chairman, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio. He has made wide-ranging and far-reaching contributions to multivariate statistics. His fundamental contributions in multivariate statistics include: multivariate distribution theory; elliptically contoured distributions; matrix valued multivariate statistics; skew-multivariate distributions and modeling to mention a few which are key for the underlying developments and tools for high-dimensional data mining.
Prior to coming to Bowling Green he had been a faculty member of the University of Michigan and the University of Arizona. He has also been a Visiting Professor at the Universities of Campinas (Brazil), Ohio State, Ghana( West Africa ), Windsor (Canada), Antioquia (Colombia), Technical University of Warsaw (Poland), Toledo, Michigan (Biostatistics), CIMAT (Mexico) ,National Sun-Yat Sen Universitsy , and Tsing-Hua University (Taiwan). During the Fall 1981 he served as the United Nation's Statistical Consultant in Ghana. He visited the University of Rajasthan during the Fall 1983 as the University Grants Commission Senior Fellow. Dr. Gupta has served on many editorial boards of several scientific journals including the J of Statistical Planning and Inference, Ohio J. of Science, Communications in Statistics, Test, Random Operators and Stochastic Equations and others. He also serves as the Series Editor for the Statistics Books and Monographs from Chapman and Hall/CRC.He has organized many conferences including the Research Conference on Jackknife and Bootstrap Methods in Statistics in 1980 , which was funded by the National Science Foundation . He is a prolific author and researcher ,having authored six books and edited eight books .In addition he has published more than three hundred research papers in reputed journals making significant contributions to the Multivariate Statistical Analysis ,Distribution Theory,Asymptotic Inference ,Robustness,Statistical Inference ,Change-Point Analysis,Modeling and Model Selection. In 1990 he was honored with the Olscamp Research Award by the Bowling Green State University for his outstanding research accomplishments. He has been a Visiting Lecturer, SIAM, 1981-83, and COPSS, 1988-90.
Dr. Gupta is a member of a large number of scientific societies and a frequent speaker on his areas of interest both in the U.S.A. and abroad. He is a Fellow of the American Statistical Association, the Institute of Statisticians, Royal Statistical Society, Ohio Academy of Science, and an elected Member of the International Statistical Institute. He has consulted for many organizations in the U.S.A. and abroad .He served in Ghana as Statistical Consultant for the United Nations.