Liu:   Center-outward ordering of multivariate data by data depth.

The recent advances in computer technology have facilitated 
greatly the collection of large scale high dimensional data, 
and statisticians face increasingly the task of analyzing 
large multivariate datasets. The classical multivariate 
analysis is well developed, but its applicability is somewhat
restricted by its intrinsic elliptical nature. A nonparametric 
alternative developed based on the concept of data depth 
will be the focus of this talk. 

A {\it data depth} is a measure of how deep or how central a 
given point is with respect to a multivariate distribution. It 
can lead a center-outward ordering of multivariate data and 
give rise to a systematic nonparametric multivariate analysis. 
The depth ordering also provides a new set of parameters which 
quantify easily the many complex multivariate features of the 
underlying distribution. These parameters can be expressed 
by simple one-dimensional graphs and be visualized easily. 
Applications of data depth and the depth ordering include 
constructions of confidence regions, determinations of P-values 
for general multivariate testing, regression, multivariate rank 
tests, and multivariate statistical quality control. Some of 
these applications will be demonstrated in an aviation safety 
analysis of some airline performance data collected by the FAA.