A0919
Title: On efficient dimension reduction with respect to the interaction between two response variables
Authors: Wei Luo - Zhejiang University (China) [presenting]
Abstract: The theory and the methodologies for dimension reduction concerning the interaction between two response variables are proposed. This is crucial for effective dimension reduction in applications such as missing data analysis and causal inference. The concepts of the locally and the globally efficient dimension reduction subspaces are introduced, which induce reduced predictors that preserve the critical feature for subsequent data analysis. These spaces can be low dimensional when neither of the two individual response variables is equipped with low-dimensional data structures, for which they cannot be recovered by the existing dimension reduction applications in general. Based on the current inverse regression methods, a family of dimension reduction methods is proposed called the dual inverse regression, which consistently estimates the locally efficient dimension reduction subspaces under mild assumptions and consistently estimates the globally efficient dimension reduction subspace when it exists. These methods are also easily implementable. In addition, a sufficient and necessary condition for the existence of the globally efficient dimension reduction subspace that is handy to check is proposed. Simulations studies and a real data example illustrate the usefulness of the proposed dual inverse regression methods.
