A0428
Title: Some theory about efficient dimension reduction with respect to interaction between two responses
Authors: Wei Luo - Zhejiang University (China) [presenting]
Abstract: Efficient dimension reduction with respect to the interaction between two response variables, which facilitates statistical analysis in multiple important application scenarios, was initially discussed in a recent study. The efficient dimension reduction subspaces were introduced, and, under mild conditions on the predictor, they were equated with the family of dual inverse regression subspaces. Besides the general framework, however, limited theory has been proposed to uncover the mystery of these spaces. A thorough characterization of the family of dual inverse regression subspaces is proposed, including their uniform lower and upper bounds, their explicit forms, their consistent and exhaustive estimation, some interesting special cases, and certain subfamilies that have desired sparsity. In addition, some of these results are extended to provide more insights into the efficient dimension reduction subspaces under the general settings, including their uniform lower and upper bounds and the sufficient and necessary conditions for the uniqueness of the space that are assessable in practice. These results largely complete the theoretical foundation for the new type of dimension reduction and, as such, enhance its applicability in statistical problems such as missing data analysis and causal inference; the latter is illustrated by simulation studies and a real data example at the end.
