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Summary of research interests
Dr. Richards' research interests include the following
areas:
Multivariate Statistical Analysis: In discriminant
analysis, where observations are to be classified among
several groups, it is necessary to study the probability
distribution of discriminant functions. In multivariate
data analyses exhibiting monotone missing data patterns
and for which the sample sizes are small, the distributions
of maximum likelihood estimators are of basic interest.
In both of these problems, Dr. Richards and his co-authors
have developed approaches for studying the distributions
of these test statistics.
Generalized Specialized Functions: Dr. Richards
is involved in a program of research to investigate
hypergeometric functions defined by matrix spaces. This
program, which is motivated by problems in multivariate
statistical analysis, has led to generalizations of
results well-known for the classical special functions.
This line of work relies heavily on representation theory
and harmonic analysis, and has led to basic research
in those areas.
Probability Inequalities: The algebraic and
analytic techniques utilized in Dr. Richards' work on
multivariate statistical analysis, generalized special
functions, and harmonic analysis are closely related
to his research in total positivity and probability
inequalities, e.g. new concepts of total positivity
germane to the theory of finite reflection groups, and
correlation inequalities of FKG type, motivated by problems
in statistics, probability, and mathematical physics.
Representative publications
W. Ehm, T. Gneiting, and D. St. P. Richards. 2004.
Convolution roots of radial positive definite functions
with compact support. Transactions of the American
Mathematical Society 356: 4655-4685.
G. J. Székely and D. St. P. Richards. 2004.
The St. Petersburg paradox and the crash of high-tech
stocks in 2000. The American Statistician 58:
225-231.
H. R. McFarland III and D. St. P. Richards. 2002.
Exact misclassification probabilities for plug-in normal
quadratic discriminant functions. II. The heterogeneous
case. Journal of Multivariate Analysis 77:
117-137.
R. D. Gupta and D. St. P. Richards. 2001. The history
of the Dirichlet and Liouville distributions. International
Statistical Review 69: 433-446.
K. I. Gross and D. St. P. Richards. 1995. Total positivity,
finite reflection groups and a formula of Harish-Chandra.
Journal of Approximation Theory 82: 60-87.
I. Lu and D. St. P. Richards. 1993. Random discriminants.
The Annals of Statistics 21: 1982-2000.
Last updated: 26
April 2005 |
