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.