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 |
