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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, May 16, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Marshall Bern}
\centerline{\sl XeroxParc.}
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\centerline{\bf Regression Depth}
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Linear regression asks for the best fit of a hyperplane to a set of n data
points in d dimensions.
I'll talk about a robust, non-metric criterion for goodness of fit called
``regression depth'', first introduced by Rousseeuw and Hubert. The
regression depth of a hyperplane H is defined to be the minimum
number of data points that H must pass through in a rotation to vertical.
I'll prove that deep hyperplanes always exist, and show how to generalize
regression depth to fitting k-flats to points, for example,
fitting a line to points in $R^3$. The proof uses some techniques from
combinatorial geometry and topology.

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