Estimation of High-dimensional Covariance Matrix
- Date: 04/10/2008
Jianqing Fan (Princeton University)
Simon Fraser University
High dimensionality comparable to the sample size is a common feature in portfolio allocation, risk management, genetic network and climatology. In this talk, we first use a multi-factor model to reduce the dimensionality and to estimate the covariance matrix for portfolio allocation and risk assessment. The impacts of dimensionality on the estimation of covariance matrix and its inverse are examined. We identify the situations under which the factor approach can gain substantially the performance and the cases where the gains are only marginal, in comparison with the sample covariance matrix. Furthermore, the impacts of the covariance matrix estimation on portfolio allocation and risk management are studied. Viable covariance modeling and sparse and robust portfolio allocations are recommended based on our mathematical results.
In other class of problems such as genetic network or climatology, sparsity of the covariance matrix or its inverse arises naturally. We then estimate high-dimensional covariance matrices using the penalized likelihood method to explore the sparsity. New algorithms are proposed. Optimal rates of convergence, sparsistency, and asymptotic normality are established. Our theoretical results are verified by simulation studies and illustrated by several applications.
About the Speaker
Professor Jianqing Fan obtained his Ph.D from the Department of
Statistics, University of California-Berkeley in1989. His recent
research interest includes bioinformatics and finance in addition to
his continued interest in more traditional statistical theory and
methodology. His earlier work on the local polynomial regression is
widely cited and has firmly established his status in statistics from
the very beginning of his research career. He is a fellow of Institute
of Mathematical Statistics and the American Statistical Association. He
was the recipient of the 2000 Presidents’ Award (The Presidents' Award,
established in 1976, is jointly sponsored by the American Statistical
Association, the Institute of Mathematical Statistics, the Biometric
Society and the Statistics Society of Canada), to an outstanding
statistician under age 40. He is recently recognized for his
accomplishment in applied mathematics, statistics with the Morningside
Gold Medal of Applied Mathematics at the Fourth International Congress
of Chinese Mathematicians. The medals are presented every three years
to outstanding mathematicians of Chinese descent under age 45.
Professor Fan served as the co-editor of the Annals of Statistics, one
of the most prestigious journals in statistics, and is currently the
President of the Institute of Mathematical Statistics. For more
information and the latest research results of Professor Fan, we
recommend his personal website which is always up to date.
Lunch will be served after the presentation.
No registration is necessary. Please email firstname.lastname@example.org (Ramo Gencay)
or email@example.com (Jianhua Chen) if you wish to join the lunch
banquet by March 27, 2008. Lunch will be served at 12:30pm outside of
the lecture auditorium at IRMACS foyer.
Scholars and graduate students with UBC parking permits can park any of
the SFU visitor parking lots as there is reciprocity with UBC parking
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