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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big JOINT STATISTICS/BIOSTATISTICS SEMINAR}
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\centerline{4:15 p.m., Tuesday, April 13, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in the 1st Floor Lounge)}


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\centerline{\sl Christopher Genovese}
\centerline{\sl Department of Statistics}
\centerline{\sl Carnegie Mellon University}
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\centerline{\bf Confidence Sets for Nonparametric Regression, with
application to Cosmology}
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Abstract:

In this talk, I will discuss recent work on constructing confidence
balls for an unknown function in nonparametric regression problems.
The goal is to construct confidence balls in a specified metric with
(asymptotically) uniform coverage that can then be constrained by
available side information.  I'll describe two approaches.  The first
extends results by Beran and Dumbgen (1998) to wavelet bases and
weighted L2 loss.  The second, still in progress, constructs L^\infty
confidence balls -- confidence bands -- that account for bias in a
truncated basis expansion.  Our approach follows Baraud (2002) in
using a family of tests to select subspaces on which to construct the
balls.  I will demonstrate these methods through an analysis of the
Cosmic Microwave Background spectrum, which is used by cosmologists to
understand the physics of the early universe.

This is joint work with Larry Wasserman.

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