Bing Li

Bing Li

Associate Professor of Statistics

Ph.D.: University of Chicago, 1992

Dr. Li's main research areas include, first, the quasi-likelihood functions and estimating equations; second, the second-order theories of statistical inference. In the first area, he has focussed on the studies of the likelihood-type functions and their use in estimating equations. Using these functions, he has established the consistency for general estimating equations, namely, that for many estimating equations, it is possible to construct a projected log likelihood ratio, each of whose minimax point is a consistent estimator. This is a more specific consistency result than those previously existed, which in the main only asserted the existence of consistent solutions. In a related work, jointly, with Peter McCullagh, Dr. Li studied a class conservative estimating equations, and investigated the properties and applications of their potential functions for inference purposes. Another problem he has studied (with Bruce Lindsay) is to construct a likelihood-type function for testing hypotheses in longitudinal data analysis, in the presence of many nuisance parameters, without estimating those parameters. As regards the second area, Dr. Li has collaborated with Bruce Lindsay in an investigation of the second-order property of the observed Fisher information. In particular, they have demonstrated that the inverse of the observed Fisher information is the best estimator, among a wide class of estimators, of the realized squared error of the maximum likelihood estimate.

With main efforts devoted to the above problems, Dr. Li is also interested in several other related, but different, areas, which include: Laplace expansions of marginal posterior densities, Minimax robust estimators, Nonparametrics, and Projected partial likelihood for life-history data.

Representative Publications:

[1] Wong, W.H. & Li, B. (1992). Laplace expansion for posterior densities of non- linear functions of parameters. Biometrika 79, page 393-8.

[2] Li, B. (1993). A deviance function for the quasi-likelihood method. Biometrika 80, page 741-753.

[3] Li, B. & McCullagh, P. (1994). Conservative estimating functions and potential functions. Annals of Statistics 22, page 340-356.

[4] Murphy, S. & Li, B. (1995). Projected partial likelihood and its application to longitudinal data. Biometrika 82, page 399-406.

[5] Li, B. & Lindsay, B. (1995). Chi-square tests for generalized estimating equations with possibly misspecified weights. To appear in Scandinavian Journal of Statistics.

[6] Li, B. (1995). A minimax approach to consistency and efficiency for estimating equations. To appear in Annals of Statistics.