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Project Information

ROBUST MULTIVARIATE STATISTICS: BEYOND ELLIPTICITY AND AFFINE EQUIVARIANCE

Agency:
NSF

National Science Foundation

Project Number:
0906773
Contact PI / Project Leader:
TYLER, DAVID E
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
The concepts of affine equivariance and elliptically symmetric distributions have played a central role in the development of robust multivariate statistical methods over the past 30 years. Statistical methods which are robust over the class of elliptical distributions are more widely applicable than methods based solely on the multivariate normal distribution. The class of elliptical distributions, though, represents only a small class of multivariate models. Important cases which do not fall within this class are mixture models and independent components models. Affine equivariance is a useful property since methods possessing it behave equally well over different covariance structures. However, there are many cases where interest lies in certain type of covariance structures, e.g. factor analysis models. The investigator's research goals are thus two-fold. First, the investigator is to further develop and study "invariant coordinate selection." This is a new multivariate method, recently introduced by the investigator, which is well suited for exploring non-elliptical models. In particular, it can be used to uncover Fisher's linear discriminant subspace for mixture models when the group identifications are unknown, and can be use to uncover the independent components in independent components models. Second, the investigator is to study the properties of certain non-affine equivariant methods, such as orthogonal equivariant M-estimates. The primary goal here is to achieve a better understanding of the type of covariance structures for which such methods may or may not be advantageous.

The need to analyze multivariate data arises in many diverse disciplines, such as computer science, psychology, meteorology, sociology, biology, econometrics and engineering. The primary interest in such data typically is not with an understanding of each variable separately, but rather with the interrelationships among the variables or with unmeasurable "latent" variables. Many common methods employed in these areas are based upon the multivariate normal model, which are now well known to perform poorly if the normal model does not hold. In particular, only a few errors in the data or a slight deviation in the model can highly influence the interpretation of an experiment or a data set, sometimes with disastrous consequences. This is particularly problematic with high dimensional data, i.e. data consisting of many variables, since bad data points or deviations from the model can be difficult to detect whenever they are associated not with just one variable but with a number of the variables. Thus, multivariate methods which are not greatly affected by such problems are crucial to a proper analysis of such data. The investigator anticipates that the intended research will have an important impact not only on steering the direction of research within robust statistics, but also on the methodology used within the many disciplines that routinely deal with multivariate data.
Project Terms:
Affect; Area; base; Biology; computer science; Data; Data Set; Development; Discipline; Engineering; Factor Analysis; falls; Goals; Group Identifications; interest; Meteorology; Methodology; Methods; Modeling; Multivariate Analysis; Normal Statistical Distribution; Play; Property; Psychology; Research; Research Personnel; research study; Role; Sociology; Statistical Methods; statistics; Structure

Details

Contact PI / Project Leader Information:
Name:  TYLER, DAVID E
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  NEW BRUNSWICK    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2009
Award Notice Date: 15-May-2009
DUNS Number: 001912864
Project Start Date: 01-Jun-2009
Budget Start Date:
CFDA Code: 47.049
Project End Date: 31-May-2012
Budget End Date:
Agency: ?

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National Science Foundation
Project Funding Information for 2009:
Year Agency

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

FY Total Cost
2009 NSF

National Science Foundation

$222,207

Results

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