Variable Selection

      Functional Data Analysis

      Nonparametric Smoothing Method

      Multivariate Analysis

      Quasi-Monte Carlo Method and Designs of Experiment
 

Research Interests:

Li is interested in the fields of variable selection, local modeling, functional data analysis and designs of experiment. His primary research focuses on the topics of variable selection and local modeling.

Variable selection is fundamental to statistical modeling. Many approaches in use are stepwise selection procedures, such as best subset variable selection and stepwise backward elimination, which can be expensive in computation and ignore stochastic errors in the variable selection process. In Li's works, new approaches are proposed to select significant variables for various statistical models. Based on penalized likelihood, the proposed approaches delete insignificant covariates by estimating their coefficients to be zero, and therefore simultaneously select significant variables and estimate parameters. It has shown in his works that the proposed approaches have oracle properties, namely, they work as well as if the correct submodel were known.

Li is also interested in the topic of functional data analysis. Functional data is also called as curve data. In fact, longitudinal data, repeated measurements and growth curves are special cases thereof.  In his work, local likelihood methodology was used to deal with efficient estimation for various nonparametric models. Further, nonparametric maximum likelihood ratio type of goodness of fit test is proposed for nonparametric regression models used in functional data analysis.