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Professor of Statistics 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 R. D. Gupta and D. St. P. Richards. 2001. The history of the Dirichlet and Liouville distributions. International Statistical Review 69, 433-446. H. R. McFarland III and D. St. P. Richards. 2001. Exact misclassification probabilities for plug-in normal quadratic discriminant functions. I. The equal-means case. Journal of Multivariate Analysis 77, 117-137. W. Ehm, T. Gneiting, and D. St. P. Richards. 1999. On the uncertainty relation for positive definite probability densities. II. Statistics 33, 267-286. 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. Annals of Statistics 21, 1982-2000. D. St. P. Richards. 1989. The central limit theorem on spaces of positive-definite matrices. Journal of Multivariate Analysis 29, 326-332. |