Research Interests

• General: Statistics, Probability, Applied Stochastic Processes, Asymptotic Theory

• Major Current Research Topics:
  • Robust Inference for Multivariate Distributions and Time Series with Very Heavy Tails
  • Nonparametric and Robust Multivariate Analysis and Outlier Detection via Quantile Methods
  • Probabilistic Modeling and Statistical Methods in Prostate Cancer Detection and Diagnosis

Education

• B.S., Mathematics, Georgia Institute of Technology, 1963
• Ph.D., Mathematical Statistics (minor in Public Health), University of North Carolina at Chapel Hill, 1967

Selected Honors

• Fellow, American Statistical Association, 1973
• Fellow, Institute of Mathematical Statistics, 1976
• Elected Member, International Statistical Institute, 1977
• Recipient of Humboldt-Preis (Senior Scientist Humboldt Award), Alexander von Humboldt Stiftung, Germany, "in recogition of accomplishments in research and teaching", 1985
• Award for Best Contributed Paper in Nonparametric Statistics at the 2002 Joint Statistical Meetings (in a tie with Ron Randles), awarded by Section on Nonparametric Statistics, American Statistical Association, 2003
• R. L. Anderson Lecturer, University of Kentucky, 2007

Selected Recent and Current Professional Service Activities

• Co-Organizer (with R. Liu, Y. Vardi and D. Souvaine), DIMACS Workshop on Data Depth: Robust Multivariate Analysis, Computational Geometry, and Applications, 2003
• Member, NSF Committee of Visitors (COV), for review of the Division of Mathematical Sciences, 2004
• Program Director, Programs in Statistics and Probability, Division of Mathematical Sciences, NSF, 2004-2005
• Program Chair-Elect and Program Chair, Section on Nonparametric Statistics, for 2008 Joint Statistical Meetings, American Statistical Association, 2006-2008
• Member, NSF Panel to review proposals, 2008
• Associate Editor, Journal of Multivariate Analysis, 2007-present
• Associate Editor, Journal of Nonparametric Statistics, 2007-present

Selected Recent and Forthcoming Talks

• Special Invited Speaker, Frontier Research in Theoretical Statistics 2000, Eindhoven, Netherlands, 2000
• Invited Participant and Speaker, Workshop on Nonparametrics 2001, Berne, Switzerland, 2001
• Keynote Speaker, 2002 Robert Bohrer Memorial Workshop for Student Papers in Statistics, University of Illinois at Urbana-Champaign, 2002
• Invited Speaker, Fourth International Conference on Statistical Analysis Based on the L1-Norm and Related Methods, Neufchatel, Switzerland, 2002
• Keynote Speaker, DIMACS Workshop on Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications, DIMACS, Rutgers University, 2003
• Invited Speaker, International Conference on Robust Statistics (ICORS), Beijing, July 2004
• Invited Speaker, International Workshop on Nonparametric Statistical Methods, Tampere, Finland, June 2005
• Lead author on presentation, "Cancer detection rate and grade shift in PCPT are reflections of finasteride-induced changes in prostate volume and tumor shrinkage: results of a mathematical modeling study", Refereed Abstract, Poster, Annual Meeting of American Urological Association, May 2006
  • This presentation was highlighted in a feature article, "Links probed between prostate volume, cancer prediction", by Cheryl Guttman, in the Urology Times, September 1, 2006. Content from the presentation was also incorporated into a Continuing Medical Education (CME) supplement to the same issue, "Update on Prostate Health", prepared with input from the lead author.
• Invited Speaker, Session on Robust and Nonparametric Analysis, WNAR/IMS Meeting, June 2006
• Invited Speaker, International Symposium on Nonparametric Statistics, sponsored by Fields Institute, Ottawa, September 2006
• 2007 R. L. Anderson Lecturer, Department of Statistics, University of Kentucky, April 2007
• Main Lecturer (4 lectures -- complete presentation), Annual Conference of Statisticians in Finland, Tampere, Finland, May 2007
• "Modeling Prostate Cancer Detection Probability" (pdf), Joint Statistical Meetings, Salt Lake City, August 2007
• Invited Talk, "Robust Nonparametric Multivariate Outlier Identification" (pdf, revised and expanded 02/24/09), Joint Statistical Meetings, Denver, August 2008
• Invited Talk, "On Equivariance/Invariance Properties of Multivariate Quantile and Related Functions, and the Role of Standardization" (pdf, updated 6/14/09), Workshop on Nonparametric Statistics: Refined, Redefined, Renewed, Arlington, Texas, April 2009. See article for AmstatNews (doc).
• Plenary Talk, "Target Asymptotic Problems Arising with Multivariate Sample Quantile Functions" (pdf, updated 6/14/09), International Symposium on New Directions in Asymptotic Statistics, University of Georgia, May 2009
• Invited Talk, title to be determined, Session on "Data Depth Methods in Data Mining, Clustering, and Beyond", International Conference on Nonparametric Statistics and Statistical Learning, Ohio State University, May 2010
• Invited Talk, title to be determined, Session on "Multivariate Ordering and Related Topics", Joint Statistical Meetings, August 2010

Books

• Author, Approximation Theorems of Mathematical Statistics, Wiley, 1980 (paperback edition, 2001)
  [Second edition in preparation]
• Author, Depth and Quantile Functions in Nonparametric Multivariate Analysis, Springer
  [In preparation]
• Co-editor, Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications, American Mathematical Society DIMACS Book Series, Volume 72, 2006 (with R. Y. Liu and D. L. Souvaine)
• Co-author, Placing Children in Special Education: A Strategy for Equity, National Academy Press, 1982 (with other members of the National Research Council Panel on Selection and Placement of Students in Programs for the Mentally Retarded)
• Co-editor, Reliability and Biometry: Statistical Analysis of Lifelength, SIAM, 1974 (with F. Proschan)

Recent Publications

• A large deviation theorem for U-processes. Statistics and Probability Letters 49 (2000) 181-193 (with W. Wang). (ps preprint file)
• Robust and nonparametric estimation via generalized L-statistics: theory, applications, and perspectives. In Advances in Methodological and Applied Aspects of Probability and Statistics (N. Balakrishnan,ed.), pp. 197-217. Gordon & Breach, 2000. (ps preprint file)
• On the performance of some nonparametric location measures relative to a general notion of multivariate symmetry. Journal of Statistical Planning and Inference 84 (2000) 55-79 (with Y. Zuo). (ps preprint file)
• General notions of statistical depth function. Annals of Statistics 28 (2000) 461-482 (with Y. Zuo). (ps preprint file)
• Structural properties and convergence results for contours of sample statistical depth functions. Annals of Statistics 28 (2000) 483-499 (with Y. Zuo). (ps preprint file)
• Nonparametric notions of multivariate "scatter measure" and "more scattered" based on statistical depth functions. Journal of Multivariate Analysis 75 (2000) 62-78 (with Y. Zuo). (ps preprint file)
• Robust and efficient estimation of the tail index of a one-parameter Pareto distribution. North American Actuarial Journal 4 (2000) 12-27 (with V. Brazauskas). (ps preprint file)
• Robust estimation of tail parameters for two-parameter Pareto and exponential models via generalized quantile statistics. Extremes 3 (2000) 231-249 (with V. Brazauskas). (ps preprint file)
• Small sample performance of robust estimators of tail parameters for Pareto and exponential models. Journal of Statistical Computation and Simulation 70 (2001) 1-19 (with V. Brazauskas). (ps preprint file)
• Shot noise on cluster processes with cluster marks, and studies of long range dependence. Advances in Applied Probability 33 (2001) 631-651 (with F. Ramirez-Perez). (ps preprint file)
• Quantile functions for multivariate analysis: approaches and applications. Statistica Neerlandica 56 (2002) 214-232. (ps preprint file)
• Generalized quantile processes based on multivariate depth functions, with applications in nonparametric multivariate analysis. Journal of Multivariate Analysis 83 (2002) 232-247. (ps preprint file)
• A depth function and a scale curve based on spatial quantiles. In Statistical Data Analysis Based on the L1-Norm and Related Methods (Y. Dodge, ed.), pp. 25-28. Birkhaeuser, 2002. (pdf updated postprint file)
• Efficient and robust fitting of lognormal distributions. North American Actuarial Journal 6 (2002) 95-109. (pdf preprint file)
• Asymptotic normality of shot noise on Poisson cluster processes with cluster marks. Journal of Probability and Statistical Science 1 (2003) 157-172 (with F. Ramirez-Perez). (pdf preprint file)
• Favorable estimators for fitting Pareto models: a study using goodness-of-fit measures with actual data. ASTIN Bulletin 33 (2003) 365-381 (with V. Brazauskas). (pdf preprint file)
• Nonparametric multivariate descriptive measures based on spatial quantiles. Journal of Statistical Planning and Inference 123 (2004) 259-278. (pdf preprint file)
• Some perspectives on location and scale depth functions. Journal of the American Statistical Association 99 (2004) 970-973. (pdf preprint file) [Invited and refereed discussion to I. Mizera and C. H. Mueller's paper, "Location-scale depth (with discussion)" (see Mizera's "Location-Scale Depth" webpage), Journal of the American Statistical Association 99 (2004) 949-989]
• Multivariate generalized spatial signed-rank methods. Journal of Statistical Research 39 (2005) 25-48 (with J. Mottonen and H. Oja). (pdf preprint file)
• Nonparametric multivariate kurtosis and tailweight measures. Journal of Nonparametric Statistics 17 (2005) 441-456 (with J. Wang). (pdf preprint file)
• Extremal point queries with lines and line segments and related problems. Computational Geometry: Theory and Applications, 32 (2005) 223-237 (with O. Daescu). (pdf preprint file)
• Depth functions in nonparametric multivariate inference. In Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications (R. Y. Liu, R. Serfling, D. L. Souvaine, eds.), pp. 1-16. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 72, American Mathematical Society, 2006. (pdf preprint file)
• On scale curves for nonparametric description of dispersion. In Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications (R. Y. Liu, R. Serfling, D. L. Souvaine, eds.), pp. 37-48 (with J. Wang). DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 72, American Mathematical Society, 2006. (pdf preprint file)
• Influence functions for a general class of depth-based quantile functions. Journal of Multivariate Analysis 97 (2006) 810-826 (with J. Wang). (pdf preprint file)
• Multivariate symmetry and asymmetry. In Encyclopedia of Statistical Sciences, Second Edition (S. Kotz, N. Balakrishnan, C. B. Read and B. Vidakovic, eds.), Vol. 8, pp. 5338-5345. Wiley, 2006. (pdf preprint file)
• Quantifying the Impact of Prostate Volumes, Numbers of Biopsy Cores, and 5alpha-Reductase Inhibitor Therapy on the Probability of Prostate Cancer Detection Using Mathematical Modeling. Journal of Urology 177 (2007) 2352-2356 (with M. J. Shulman, G. L. Thompson, Z. Xiao, E. A. Benaim, C. G. Roehrborn, and R. Rittmaster). (pdf) (Final preprint version pdf) (Full Unabridged Version, February 2006 pdf)
  • See also the editorial on this paper in the same issue: Alan S. Kibel. Optimizing Prostate Biopsy Techniques. Journal of Urology 177 (2007) 1976-1977 (pdf)
• High Grade Prostate Cancer in the Prostate Cancer Prevention Trial: Fact or Artifact? Journal of the National Cancer Institute 99 (2007) 1355-1356, Invited editorial (with G. L. Andriole, P. A. Humphrey, and R. L. Grubb). (pdf)
• A Contribution to Multivariate L-Moments: L-Comoment Matrices. Journal of Multivariate Analysis 98 (2007) 1765-1781 (with P. Xiao). (pdf preprint file) (Full Unabridged Version pdf) (copy of published version available upon request)
  • Talk Presentation, "Multivariate Extension of L-Moments via L-Comoments, and Applications" (pdf), Joint Statistical Meetings, Denver, August 2008
  • Links to Useful Sources on L-Moments and L-Comoments
• Survey on (some) nonparametric and robust multivariate methods. Proceedings of 2007 Conference of Finnish Statisticians, in The Yearbook of the Finnish Statistical Society 2007 (2008) 11-41. (pdf preprint file)
• Multivariate spatial U-quantiles: a Bahadur-Kiefer representation, a Theil-Sen estimator for multiple regression, and a robust dispersion estimator. Journal of Statistical Planning and Inference 138 (2008) 1660-1678 (with W. Zhou). (pdf preprint file) (copy of published version available upon request)
• Generalized multivariate rank type statistics via spatial U-quantiles. Statistics and Probability Letters 78 (2008) 376-383 (with W. Zhou). (pdf preprint file)
• Influence functions of some depth functions, and application to depth-weighted L-statistics. Journal of Nonparametric Statistics 21 (2009) 49-66 (with Xin Dang and Weihua Zhou). (pdf preprint file)
• Inequalities relating addition and replacement type finite sample breakdown points. International Journal of Statistical Sciences 9 (Special Issue on Nonparametric Statistics in Honor of Professor A. K. Md. Ehsanes Saleh) (2009) 71-83 (pdf preprint file)
• Exponential probability inequality and convergence results for the median absolute deviation and its modifications. Statistics and Probability Letters 79 (2009) 1767-1773 (with Satyaki Mazumder). (pdf preprint file)
• Bahadur representations for the median absolute deviation and its modifications. Statistics and Probability Letters 79 (2009) 1774-1783 (with Satyaki Mazumder). (pdf preprint file)
• Nonparametric depth-based multivariate outlier identifiers, and masking robustness properties. Journal of Statistical Planning and Inference 140 (2010) 198-213 (with Xin Dang). (pdf preprint file)
• A numerical study of multiple imputation methods using nonparametric multivariate outlier identifiers and depth-based performance criteria with clinical laboratory data. Journal of Statistical Computation and Simulation, 2009, in press (with Xin Dang). (pdf preprint file)
• Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardization. Journal of Nonparametric Statistics, 2009, in press (pdf preprint file)
• Some perspectives on multivariate quantile and depth functions. Annals of Statistics, 2009, in press (with Y. Zuo). [Invited and refereed discussion to Marc Hallin, Davy Paindaveine, and Miroslav Siman's paper, "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth (with discussion)", Annals of Statistics, 2009, in press]
• Asymptotic relative efficiency in estimation. Invited entry for International Encyclopedia of Statistical Science, Miodrag Lovric (Ed.), Springer, 2010, to appear. (pdf preprint file)

Recent and Current Contract and Grant Support

• PI, "Robust Methods in Actuarial Science", Society of Actuaries and Casualty Actuarial Society, 1997-1999
• PI, "Multidimensional Depth Functions, Multidimensional Generalized L-Statistics, and Related Procedures", National Science Foundation, 1997-2001
• PI, "Robust and Efficient Fitting of Loss Models", Society of Actuaries, 2000-2002
• PI, "Nonparametric and Robust Multivariate Analysis via Quantile Functions", National Science Foundation, 2001-2008
• PI, Supplemental Funding for above NSF Grant, National Science Foundation, 2004
• PI, "Mathematical Modeling and Testing of the Relationship of Prostate Gland Volume to Prostate Cancer Detection Rate", GlaxoSmithKline, 2004-2005
• Co-PI (with Ovidiu Daescu), "Outlier Identification and Handling in Computational Geometry Problems", National Science Foundation, 2004-2006
• PI, "Extended Mathematical Modeling and Testing of the Relationship of Prostate Gland Volume to Prostate Cancer Detection Rate, Fraction of Positive Biopsy Cores, and Volume of Cancer Found", GlaxoSmithKline, 2006-2007
• PI, "Multivariate Modeling in Actuarial Science Allowing Heavy Tailed Distributions, via the L-Moments/L-Comoments Approach", The Actuarial Foundation, 2007-2009
• PI, "Foundations for Multivariate and Time Series Analysis with Heavy Tailed Data via L-Comoments", National Security Agency, 2008-2010
• PI, "Nonparametric Outlyingness and Descriptive Measures in Multivariate and General Data Settings", National Science Foundation, 2008-2011
• PI, "Supplemental Funding for above NSF Grant, National Science Foundation, 2009

Recent and Current Doctoral Students and Dissertation Topics

• Yijun Zuo, Contributions to Theory and Applications of Statistical Depth Functions, 1998 (Professor, Department of Statistics and Probability, Michigan State University)
• Vytaras Brazauskas, Robust and Nonparametric Methods for Pareto Tail Index Estimation, with Actuarial Science Applications, 1999 (Associate Professor, Department of Mathematics, University of Wisconsin at Milwaukee)
• Filemon Ramirez-Perez, Contributions to Shot Noise on Cluster Processes with Cluster Marks, 2000 (Associate Professor, Area de Estadistica, Departamento de Fitotecnia, Universidad Autonoma Chapingo, Mexico)
• Zhenwu Chen, Trimmed and Winsorized M- and Z-Estimators, with Applications to Robust Estimation in Neural Network Models, 2000 (Senior Scientist, Texas Instruments, Dallas, Texas)
• Jin Wang, On Nonparametric Multivariate Scale, Kurtosis, and Tailweight Measures, 2003 (Associate Professor, Department of Mathematics and Statistics, Northern Arizona University)
• Xin Dang, Nonparametric Multivariate Outlier Detection Methods, with Applications, 2005 (Assistant Professor, Department of Mathematics, University of Mississippi)
• Weihua Zhou, Multivariate Spatial U-Quantiles: Theory and Applications, 2005 (Assistant Professor, Department of Mathematics and Statistics, University of North Carolina at Charlotte)
• Peng Xiao, Contributions to Multivariate L-Moments: L-Comoment Matrices, 2006 (Assistant Professor, Department of Mathematics, East Carolina University)
• Satyaki Mazumder, Topic to be selected in the area of Robust Nonparametric Multivariate Analysis, anticipated graduation Summer 2010

Recent Teaching

• Spring 2006
  • STAT 5352 Probability and Statistics II
  • STAT 4352 Mathematical Statistics II
  • STAT 6344 Probability Theory I
• Fall 2006
  • STAT 3332 Statistics for Life Sciences
  • STAT 7345 Advanced Probability and Stochastic Processes
• Spring 2007
  • STAT 3332 Statistics for Life Sciences
  • STAT 7334 Nonparametric and Robust Statistical Methods
• Fall 2007
  • STAT 3332 Statistics for Life Sciences
  • STAT 6331 Statistical Inference I
• Spring 2008
  • STAT 3332 Statistics for Life Sciences
  • STAT 6390 Topics in Statistics: "Outlier Identification and Handling in Statistical Applications"
• Fall 2008
  • On sabbatical, no organized teaching.
• Spring 2009
  • STAT 3332 Statistics for Life Sciences
  • STAT 7345 Advanced Probability and Stochastic Processes

Current Courses -- Fall 2009

• STAT 3332 Statistics for Life Sciences
• STAT 6331 Statistical Inference I