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 Letters49 (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 Inference84 (2000) 55-79 (with Y. Zuo).
(ps preprint file)
General notions of statistical depth function.
Annals of Statistics28 (2000) 461-482 (with Y. Zuo).
(ps preprint file)
Structural properties and convergence results for contours of
sample statistical depth functions.
Annals of Statistics28 (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 Analysis75 (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 Journal4 (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.
Extremes3 (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 Simulation70 (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 Probability33 (2001) 631-651
(with F. Ramirez-Perez).
(ps
preprint file)
Quantile functions for multivariate analysis: approaches and applications.
Statistica Neerlandica56 (2002) 214-232.
(ps
preprint file)
Generalized quantile processes based on multivariate depth functions,
with applications in nonparametric multivariate analysis.
Journal of Multivariate Analysis83 (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 Journal6 (2002) 95-109.
(pdf
preprint file)
Asymptotic normality of shot noise on Poisson cluster processes
with cluster marks.
Journal of Probability and Statistical Science1 (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 Bulletin33 (2003) 365-381
(with V. Brazauskas).
(pdf preprint file)
Nonparametric multivariate descriptive measures based on
spatial quantiles.
Journal of Statistical Planning and Inference123 (2004) 259-278.
(pdf
preprint file)
Some perspectives on location and scale depth functions.
Journal of the American Statistical Association99 (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 Association99 (2004) 949-989]
Multivariate generalized spatial signed-rank methods.
Journal of Statistical Research39 (2005) 25-48 (with J. Mottonen and H. Oja).
(pdf
preprint file)
Nonparametric multivariate kurtosis and tailweight measures.
Journal of Nonparametric Statistics17 (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 Analysis97 (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 Urology177 (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 Urology177 (2007) 1976-1977
(pdf)
High Grade Prostate Cancer in the Prostate Cancer Prevention Trial: Fact or Artifact?
Journal of the National Cancer Institute99 (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 Analysis98 (2007) 1765-1781
(with P. Xiao).
(pdf preprint file)
(Full Unabridged Versionpdf)
(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
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 Inference138 (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 Letters78 (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 Statistics21 (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 Sciences9
(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 Letters79 (2009) 1767-1773
(with Satyaki Mazumder).
(pdf
preprint file)
Bahadur representations
for the median absolute deviation and its modifications.
Statistics and Probability Letters79 (2009) 1774-1783
(with Satyaki Mazumder).
(pdf preprint file)
Nonparametric depth-based multivariate outlier identifiers, and masking robustness properties.
Journal of Statistical Planning and Inference140 (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]
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