B1701
Title: On efficient dimension reduction with respect to the interaction between two response variables
Authors: Wei Luo - Zhejiang University (China) [presenting]
Abstract: Novel theory and methodologies for dimension reduction are introduced with respect to the interaction between two response variables, which is a new research problem that has wide applications in missing data analysis, causal inference, and graphical models, etc. We formulate the parameters of interest to be the locally and the globally efficient dimension reduction subspaces, and justify the generality of the corresponding low-dimensional assumption. We then construct estimating equations that characterize these parameters, using which we develop a generic family of consistent, model-free, and easily implementable dimension reduction methods called the dual inverse regression methods. We also build the theory regarding the existence of the globally efficient dimension reduction subspace, and provide a handy way to check this in practice. The proposal differs fundamentally from the literature of sufficient dimension reduction in terms of the research interest, the assumption adopted, the estimation methods, and the corresponding applications, and it potentially creates a new paradigm of dimension reduction research. Its usefulness is illustrated by simulation studies and a real data example at the end.
