Spring 2001 Seminar Series - February 27, 2001
University of Minnesota
School of Statistics
College of Liberal Arts
Change-point Problem
Wei Biao Wu
University of Michigan
(Statistics Search Candidate)
Tuesday, February 27, 2001
4:00 PM,
211
Vincent Hall
Minneapolis, East Bank Campus
Social at 3:30 PM,
300
Ford Hall
Abstract
Many time series can be modeled as the sum of three components: long-time trend,
seasonal effect and background noise. The trend superimposed with the seasonal
effect constitute the mean of the process. The issue of mean stationarity is
usually the first step for further statistical inference. In this talk, we
present a theory of testing and estimation for a monotonic trend and the
identification of seasonal effects. Testing is cast as a generic change-point
problem, or probabilistic diagnostics. The change-point problem has been one of
the central issues of statistical inference for several decades. It includes,
for example, testing for changes in weather patterns and disease rates. We are
mainly concerned with a posteriori testing, using spectral analysis to
determine periodic components and isotonic regression to estimate the trend.
A distinctive feature of our approach is that these two problems can be treated
simultaneously: isotonic regression gives estimators for long-time trend with
negligible influence from seasonal effects.