Research

Research supported as the Principal Investigator (PI) by the National Science Foundation grant (NSF DMS-1404891, 2014-2018), Research Board Awards (RB15004, 2014-2017; RB17092, 2017-2018) and a start-up grant from UIUC.

Research Overview

I am currently interested in the analysis of high-dimensional multiple time series data. Statistical estimation and inference for high-dimensional time dependent data are notoriously difficult and challenging since (i) the temporal dependence is nonlinear; (ii) the underlying data structures are quite complicated in high-dimensions; (iii) the observations may have heavier tails than subgaussian distributions; and (iv) the data generation mechanism may exhibit certain dynamic features. My research work focuses on a broad spectrum of the second-order estimation and inference problems for high-dimension time series including estimation of the space-time covariance matrix, time-varying graphical models, and their related functionals and latent structures.

On the application side, my theoretical and methodological work provides the guidance for a wide range of modern applications in the spatiotemporal Big Data analytics such as construction of brain connectivity networks using functional Magnetic Resonance Imaging (fMRI) data and some applied econometrics problems.

Collaborators (alphabetical)

Young-Heon Kim (Mathematics, UBC)
Roger Koenker (Economics, UIUC)
Martin McKeown (Medicine (Neurology), UBC)
Z. Jane Wang (ECE, UBC)
Wei Biao Wu (Statistics, U. Chicago)
Mengyu Xu (Statistics, University of Central Florida)

Students
Mengjia Yu (Ph.D. in progress)

Alumni
Yifeng He (Ph.D. 2017, first job: biostatistician at Incyte)
Xin Ding (M.Sc. 2016, first job: Ph.D. student at UBC Department of Statistics)

Invited Talks

  • Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications.  2017 International Chinese Statistical Association Applied Statistics Symposium. Chicago, IL, June 28, 2017.
  • Gaussian approximation and bootstrap theorems for high-dimensional U-statistics. The 10th ICSA International Conference on Global Growth of Modern Statistics in the 21st Century. Shanghai, China, December 22, 2016.
  • Gaussian and bootstrap approximations of high-dimensional U-statistics and their applications. Department of Statistics and Actuarial Science Colloquia. The University of Iowa, Iowa City, IA, November 3, 2016.
  • Regularized estimation of linear functionals for high-dimensional time series. 2016 NBER/NSF Time Series Conference. Columbia University, New York City, NY, September 17, 2016.
  • Regularized estimation of linear functionals for high-dimensional time series. ICSA Midwest Chapter Annual Meeting 2015. Chicago, IL, October 26, 2015.
  • Estimating time-varying networks for high-dimensional time series. Joint Statistical Meetings, Seattle, WA, August 12, 2015.
  • Inference of high-dimensional linear models with time-varying coefficients. IEEE Signal Processing Society Vancouver Chapter, University of British Columbia, BC, Canada, August 10, 2015.
  • Inference of high-dimensional linear models with time-varying coefficients. 2015 IMS-China International Conference on Statistics and Probability, Kunming, China, July 3, 2015.
  • Second-order Estimation for high-dimensional time series: time-varying networks. New Researchers Conference on High-Dimensional Statistics in the Age of Big Data. Peking University, June 28, 2015.
  • Second order inference for high-dimensional time series. 7th International conference of the ERCIM WG on computational and methodological statistics, University of Pisa, Italy, December 6, 2014.
  • Second order estimation for high-dimensional time series: covariance and precision matrices. CSL Communications Seminar, Department of ECE, UIUC, Urbana, IL, September 22, 2014.
  • Needle in a Haystack – High-dimensional covariance and precision matrix estimation and Lasso-type regressions. Illinois Informatics Institute Seminar, UIUC, Urbana, IL, November 21, 2013.
  • Covariance and precision matrix estimation for high-dimensional time series. Department of Statistics, Purdue University, West Lafayette, IN, February 6, 2013.
  • Covariance and precision matrix estimation for high-dimensional time series. Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, January 31, 2013.
  • Needle in a Haystack – High-dimensional covariance and precision matrix estimation and Lasso-type regressions. Department of Computing Science, University of Alberta, Edmonton, AB, January 22, 2013.
  • Covariance and precision matrix estimation for high-dimensional time series. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, January 22, 2013.
  • Needle in a Haystack – High-dimensional covariance and precision matrix estimation and Lasso-type regressions. Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, December 12, 2012.
  • Covariance and precision matrix estimation for high-dimensional time series. Division of Statistics Colloquium, Northern Illinois University, DeKalb, IL, November 30, 2012.
  • Covariance and precision matrix estimation for high-dimensional time series. Department of Statistics and Probability Colloquia, Michigan State University, East Lansing, MI, November 13, 2012.
  • Covariance and precision matrix estimation for high-dimensional time series. Statistics Seminar, University of Illinois at Chicago, Chicago, IL, October 3, 2012.
  • Covariance and precision matrix estimation for high-dimensional time series. Machine Learning Reading Group, Department of Statistics, University of Chicago, Chicago, IL, October 2, 2012.
  • Statistical estimation of high-dimensional sparse precision matrices. Research at TTIC, Chicago, IL, March 2, 2012.
  • Asymptotic analysis of the Huberized LASSO estimator. ICASSP’10, Dallas, TX, USA, March 17, 2010.

Research Sponsors

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