Wang’s research mainly falls into the following areas: object oriented data analysis, statistics on manifolds, and model selection. His primary research centers on developing new mathematical and statistical methods to solve many problems from various scientific research fields.

Object oriented data, such as tree-structured data, random graphs, manifold data and curve data, are frequently collected. In object oriented data analysis, Wang considered problems motivated by data from neuro-image which can be represented by a set of tree-structured objects. He studied the fundamental properties of the topological structures. Recently, Wang is particularly interested in the problem of modeling tree-structured data to explain the relationship between tree-structured covariates and numerical response, and/or between numerical covariates and tree-structured response.

In the topic of manifold learning, Wang considered the problem of manifold recovery and curvilinear feature extraction, and demonstrated the connection between nonlinear latent structure analysis and locally linear embedding.

In his recent research interest in model selection, Wang considered two different problems: Hellinger distance based model selection, and regularized spatial linear regression.