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
• Co-organizer (with Edgar Brunner and Madan Puri), Workshop on Nonparametric Statistics: Refined, Redefined, Renewed, 2009
• Co-organizer (with Mia Hubert, Jun Li, and Wolfgang Polonik), forthcoming Oberwolfach Miniworkshop on Level Sets and Depth Contours in High Dimensional Data, 2011

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", 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, "Robust, Affine Invariant, Computationally Easy Nonparametric Multivariate Outlyingness Functions", 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, "On Obtaining Affine Equivariance or Invariance of Multivariate Statistics, with Application to Quantile and Outlyingness Functions", Session on "Multivariate Ordering and Related Topics", Joint Statistical Meetings, August 2010
• Opening Talk, "Depth, Outlyingness, Quantile, and Rank Functions", Oberwolfach Workshop on Level Sets and Depth Contours in High-Dimensional Data, Oberwolfach, February 2011 pdf
• Plenary Talk, "Invariance and Equivariance: Benefits, Costs, and Methods", 4th Lehmann Symposium, May 2011 pdf
• Invited Talk, "Fitting Autoregresssive Models Allowing Outliers and Heavy Tailed Innovations", Session on "Quantile Regression, Time Series and Extremes with Applications to Business Forecasting and Risk Management", Joint Statistical Meetings, August 2011
• Invited Talk, Session on "Data Depth", 8th World Congress on Probability and Statistics, Istanbul, July 2012
• Invited Talk, "Computationally Easy Outlier Detection via Projection Pursuit with Finitely Many Directions", Session on "Data-Driven Nonparametric Statistical Methodology", Joint Statistical Meetings, August 2012

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)
• 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)
• 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, 2002. (pdf 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)
• Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardization. Journal of Nonparametric Statistics, 22 (2010) 915-936. (pdf preprint file)
• Editorial for the special issue on `Papers inspired by the workshop on "Nonparametric Statistics: Refined, Redefined, and Renewed"'. Journal of Nonparametric Statistics, 22 (2010) 821-822 (with E. Brunner and M. Puri).
• Some perspectives on multivariate quantile and depth functions. Annals of Statistics 38 (2010) 676-684 (with Y. Zuo) (reprint). [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, 38 (2010) 635-703]
• Asymptotic relative efficiency in estimation. Invited and refereed entry for International Encyclopedia of Statistical Science, Miodrag Lovric (Ed.), Springer, Part 1 (2011) 68-72. (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, 81 (2011) 547-560 (with Xin Dang). (pdf preprint file)
• Commentary on Basu (1956). Invited and refereed entry for Selected Works of Debabrata Basu, Anirban DasGupta (Ed.), Springer, 2011, 27-30. (pdf preprint file)
• Depth. Invited and refereed entry for Encyclopedia of Environmetrics, 2nd Edition, Wiley, 2011, in press. (pdf preprint file)
• A highly efficient and effective motif discovery method for ChIP-seq/ChIP-chip data using positional information. Nucleic Acids Research (2011) in press (authors: Xiaotu Ma, Ashwinikumar Kulkarni, Zhihua Zhang, Zhenyu Xuan, Robert Serfling, and Michael Q. Zhang) (pdf preprint file) (Supplementary Text 1)
• On invariant coordinate system (ICS) functionals. International Statistical Review (2011) in press (with P. Ilmonen and H. Oja). (pdf preprint file)

Submitted Papers & Papers in Revision

• A Robust Sample Spatial Outlyingness Function, July 2011, with S. Mazumder. In revision for Journal of Statistical Planning and Inference. (pdf).
• Computationally Easy Outlier Detection via Projection Pursuit with Finitely Many Directions, December 2011, with S. Mazumder. Submitted. (pdf).
• On Strong Invariant Coordinate System (SICS) Functionals. In revision (July 2009; updated June 2010; updated March 2011 pdf; currently in further development; a part of this paper is included in the paper "On Invariant Coordinate System (ICS) Functionals" above)
• Fitting Autoregressive Models via Yule-Walker Equations Allowing Heavy Tail Innovations, July 2010, (pdf). In substantial revision, with M. Carcea as additional author.
• A Mahalanobis Multivariate Quantile Function (July 2008, revised December 2008 pdf). NOTE. A part of this manuscript has now been published -- see above paper "Equivariance and invariance properties of multivariate quantile functions, and the role of standardization". The remainder is in revision and will be submitted in the near future.

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, 2004-2008
• 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, 2009-2011
• PI, "Multivariate Depth and Quantile Functions: Foundations and Applications", National Science Foundation, 2011-2014

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, Affine Invariant, Robust, and Computationally Easy Multivariate Outlier Identification and Related Methods, 2010 [For excellence in graduate studies, Dr. Mazumder received the 2010 President David Daniel Distinguished Dissertation Award, including a cash prize.] (Fellow Faculty, Indian Institute of Science, Education and Research, Kolkata, India)
• Gerald Ogola, Statistical Methods for the Interpretation of Prostate Cancer Biopsy Results, anticipated graduation Summer 2012
• Marcel Carcea, Contributions to Time Series Modeling Under Lower Order Moment Assumptions, anticipated graduation Summer 2013

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
• Fall 2009
  • STAT 3332 Statistics for Life Sciences
  • STAT 6331 Statistical Inference I
• Spring 2010
  • STAT 3332 Statistics for Life Sciences
  • STAT 7334 Nonparametric and Robust Statistical Methods
• Fall 2010
  • STAT 3332 Statistics for Life Sciences
  • STAT 7345 Advanced Probability and Stochastic Processes
• Spring 2011
  • STAT 3332 Statistics for Life Sciences
  • STAT 7331 Multivariate Analysis
• Fall 2011
  • STAT 3332 Statistics for Life Sciences
  • STAT 6348 Applied Multivariate Analysis
• Spring 2012
  • STAT 3332 Statistics for Life Sciences
  • STAT 6344 Probability Theory I

Current Courses -- Spring 2012

• STAT 3332 Statistics for Life Sciences

• STAT 6344 Probability Theory I