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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, October 3, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl S. C. Kou}
\centerline{\sl Department of Statistics}
\centerline{\sl Stanford University}
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\centerline{\bf Extended Exponential Criterion: A New Selection Procedure
For Scatterplot Smoothers}
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Nonparametric regression, such as smoothing spline, is widely used in many
scientific disciplines as a valuable data-analyzing method. The use of a
smoother requires the choice of a smoothing parameter which, by balancing
fidelity and roughness, controls how much the smoothing is done. Two
popular selection criteria to choose the smoothing parameter are
$C_p$ and generalized maximum likelihood (GML). Each, however, has its own
problem. For $C_p$ the problem is its high variability, while for GML, the
problem is its potentially big bias. In this talk we propose a new
selection procedure: the extended exponential (EE) criterion, which
combines the strength of $C_p$ and GML, yet avoids their weakness in that
the EE\ criterion has (a) small variability, (b) small bias. In addition to
these, it also has (c) small tendency toward under and oversmoothing. All
three criteria turn out to have simple geometric interpretation, which
plays a pivotal role in our finite-sample, non-asymptotic theoretical
analysis. The EE criterion is also shown to be more robust against
non-normality. In the end, some large sample results are presented.

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