Fall Seminar Series - September 9, 2004
University of Minnesota
School of Statistics
College of Liberal Arts
Local
likelihood modeling by structural adaptive smoothing
Joerg Polzehl
Weierstrass Institute of Applied Analysis and Stochastics
Berlin, Germany
Thursday, September 9, 2004
4:00 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300 Ford Hall
Abstract
Structural
adaptation provides a new approach to
edge preserving smoothing procedures. The general
idea is based on local homogeneity. The assumption that
a local model with few parameters allows for a
good approximation of an unknown regression function
in a local vicinity of each point is exploited to
both recover these vicinities and obtain local estimates.
The approach leads to an iterative procedure that allows for,
in some sense, optimal reconstruction from highly structured data.
The resulting algorithms have an interpretation
as multiscale procedures. The concept is quite general
and applies to a variety of error models.
We will illustrate the use of structural adaptation methods
with a variety of applications. These include various imaging problems
as well as, if time permits, applications to financial time series.