B1329
Title: On efficient dimension reduction with respect to the interaction between two response variables
Authors: Wei Luo - Zhejiang University (China) [presenting]
Abstract: The novel theory and methodologies for dimension reduction are proposed concerning the interaction between two response variables, a new research problem with wide applications in missing data analysis, causal inference, graphical models, etc. The parameters of interest are formulated to be the locally and the globally efficient dimension reduction subspaces and justify the generality of the corresponding low-dimensional assumption. Estimating equations are then constructed that characterize these parameters. A generic family of consistent, model-free, and easily implementable dimension reduction methods are developed called the dual inverse regression methods. The theory is also built regarding the existence of the globally efficient dimension reduction subspace, and a handy way to check this in practice is provided. The proposed work 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. Simulation studies and a real data example at the end illustrate its usefulness.
