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Bing Li


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Summary of research interests

Dr. Li's main research interests are dimension reduction, estimating equations and quasi-likelihood, and asymptotic methods.

The recent computing revolution has produced an unprecedented capacity for data processing and storage, motivated and followed by advances in a number of research fields. Dimension reduction is a powerful means to eliminate redundancy and identify informational "cores" in complex and often overwhelmingly large data sets. As such its research has gained tremendous momentum since its introduction in the early 90s. In his research, Dr. Li and coauthors first noticed the issue of nuisance parameter and the parameter of interest in dimension reduction, and proposed a theoretical framework, the Central Mean Space, as well as an iterative transformation method to estimate the parameter of interest. They developed dimension reduction methods when the predictor has a categorical component, and have advanced the asymptotic analysis of dimension reduction methods. Recently, Dr. Li and coauthors introduced a "contour regression" method that to increase the accuracy and comprehensiveness of dimension reduction.

In his research in estimating equations and quasi-likelihood, Dr. Li worked on the fundamental problem of identifying consistent solutions of estimating equations, the construction of likelihood from estimating equations for statistical inference, and the design of estimating equations whose solution has minimum asymptotic variance for both independent and longitudinal data. He has also developed nonparametric optimal estimating equations that do not require the variance assumption and at the same time dampen the noise caused by adaptation.

In asymptotic analysis, apart from the mentioned work related dimension reduction, Dr. Li has studied second-order optimality of the observed Fisher information and introduced a quasi-likelihood equation that incorporates the skewness information.

Representative Publications

Li, B., Zha, H. and Chiaromonte, F. (2005). Contour regression: a general approach to dimension reduction. Annals of Statistics. To appear.

Cook, R.D. and Li, B. (2004). Determining the dimension of Iterative Hessian Transformation. Annals of Statistics, vol 32.

Li, B., Cook, R.D., Chiaromonte, F. (2003). Dimension reduction for conditional mean in regression with categorical predictors. Annals of Statistics, vol 31, 1636-1668.

Cook , R.D. and Li , B. (2002). Dimension reduction for conditional mean in regression. Annals of Statistics, vol 30, 455-474.

Chiaromonte, F. Cook, R. D. and Li , B. (2002). Partial dimension reduction with categorical predictors. Annals of Statistics, vol 30, 475-497.

A. Qu., B. Lindsay, and B. Li. (2000). Improving generalized estimating equations using quadratic inference functions. Biometrika 87: 823-836.

B. Li. (1998). An optimal estimating equation based on the first three cumulants. Biometrika 85: 103-114.

B. Lindsay and B. Li. (1997). On second-order optimality of the observed Fisher information. Annals of Statistics 25: 2172-2199.

B. Li. (1996). A minimax approach to consistency and efficiency for estimating equations. Annals of Statistics 24: 1283-1297.

S. Murphy and B. Li. (1995). Projected partial likelihood and its application to longitudinal data. Biometrika 82: 399-406.

Li, B. and McCullagh, P. (1994). Potential functions and conservative estimating functions. Annals of Statistics, vol 22, 340-356.

B. Li. (1993). A deviance function for the quasi-likelihood method. Biometrika 80: 741-753.

Last updated: April 17, 2005

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