Spring 2002 Seminar Series - February 26, 2002
University of Minnesota
School of Statistics
College of Liberal Arts
Projection depth functions and some applications
Yijun Zuo
Arizona State University
(Statistics Search Candidate)
Tuesday, February 26, 2002
4:00 PM,
B10
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM,
300
Ford Hall
Abstract
Simple one-dimensional statistics based on ordering have played such an
important role in one-dimensional data analysis that their multi-dimensional
analogues have been sought for years, without many completely satisfactory
results. The extension to higher dimensions of these one-dimensional statistics,
such as the median, is difficult because there is no natural and unambiguous
method of fully ordering or ranking multi-dimensional observations.
Statistical depth functions are proving to be a promising tool for ordering
multi-dimensional observations. The main idea of depth functions is to provide
from the "deepest" point a "center-outward" ordering of multi-dimensional
observations. Multi-dimensional data ordering is not the only application of
depth functions, though. Depth functions have brought us new perspectives
towards multi-dimensional exploratory data analysis and inference, and have
shown to have significant applications in disciplines ranging from industrial
engineering to biomedical sciences.
In this talk, criteria for depth functions are discussed and some popular
notions of depth are examined with emphasis on projection depth. Location
and scatter estimators induced from projection depth functions are examined
with focus on their limiting distribution, robustness and efficiency. Unlike
many existing high breakdown point counterparts which are ironically not very
efficient, these estimators are proven to be able to keep a desirable balance
between robustness and efficiency. Depth based testing and confidence regions
are discussed. Other applications of depth functions (e.g., those in regression
and quality control) and computing issues are addressed.