?         Office: 5734 S. University Ave, Department of Statistics, The University of Chicago, Chicago, IL 60637

?         E-mail: wbwu@galton dot uchicago dot an educational institute

?         My homepage at University of Chicago

?         My homepage at University of Michigan


In the study of random processes, dependence plays a fundamental role. By interpreting random processes as physical systems, I introduced physical dependence coefficients that quantify the degree of dependence of outputs on inputs. Such dependence measures are related to the nonlinear system theory and riskmetrics. They provide a new framework for the study of random processes and shed new light on a variety of problems including estimation of linear models with dependent errors, nonparametric inference of time series, representations of sample quantiles, bootstrap for time series, spectral estimation among others. This work is published at Wu (October, 2005): Nonlinear system theory: Another look at dependence, Proceedings of the National Academy of Sciences.

I am currently interested in estimating covariance matrices of temporally observed series. The latter problem is quite important in the study of functional and longitudinal data. On the other hand, however, this problem is notoriously difficult since (i) one needs to estimate as many as n(n+1)/2 unknowns for a covariance matrix and (ii) a covariance matrix is intrinsically positive definite if the underlying random vector is linearly independent. This work is joint with Mohsen Pourahmadi.

Here is a list of my papers, which cover my several recent areas of interest.



National Science Foundation Career Award

National Science Foundation Research Grants

The Tjalling C. Koopmans Econometric Theory Prize, 2009

Econometric Theory Multa Scripsit Award, 2010


Eric Beutner (Maastricht University, Netherlands), X. Chen (Yale), J.M. Comeron (Dept of Biological Sciences, U. Iowa), S. Cs\"org\H{o} (U. Szeged, Hungary; Member, Hungarian Academy of Sciences), Dana Draghicescu (CUNY), H. Erdogan (EECS, U. Michigan), J.A. Fessler (EECS, U. Michigan), Bei Gou (Electrical Engineering, U. Texas Arlington), Serge Guillas (Georgia Tech.), Tailen Hsing (Statistics, U. Mich.), Y. Huang (UIUC), M. Kreitman (Ecology and Evolution, U. Chicago), Wen-Hsiung Li (Ecology and Evolution, U. Chicago), W. Liu, H.H.S. Lu (Institute of Statistics, National Chiao Tung U., Taiwan), H. Ma (EECS, U. Michigan), G. Mentz (Statistics, U. Michigan), G. Michailidis (Statistics, U. Michigan), J. Mielniczuk (Computer Science Institute, Polish Academy of Sciences), W. Min (IBM), M. Peligrad (Mathematics, U. Cincinnati), G. Mitra (Brunel U., UK), M. Pourahmadi (Statistics, TAMU), Hong Qin, C.V. Ravishankar (Computer Science \& Engineering, U. California--Riverside), K.G. Shin (EECS, U. Michigan), X. Shao (Statistics, UIUC), B. Valk\'o (R\'enyi Mathematics Institute, Hungarian Academy of Sciences), S. Utev (Mathematical Sciences, U. Nottingham, England), K.M. Wasserman (EECS, U. Mich.), M. Woodroofe (Statistics, U. Mich.), Han Xiao (Rutgers),Y. Yi (NYU), Keming Yu (Brunel U., UK) Xingbin Yu (Electric Reliability Council of Texas), Henryk Z?hle (Saarland University, Germany), D. Zhang (Qualcomm Inc., San Diego), T. Zhang (Uchicago), Zhibiao Zhao (Statistics, Penn State Univ.), Hui Zheng (Electrical Engineering, U. Texas Arlington), Zhou Zhou (UChicago)