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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, February 13, 2001}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Wei Biao Wu}
\centerline{\sl Department of Statistics}
\centerline{\sl University of Michigan}
\centerline{\sl Ann Arbor,  MI 48109}
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\centerline{\bf Change-point Problem}

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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.

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