Sufficient Dimension Folding with Categorical Predictors

• Activity Number: 520 - Variable Selection, Model Selection, and Aggregated Inference
• Type: Contributed
• Date/Time: Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Qingcong Yuan* and Yuanwen Wang and Yuan Xue
• Companies: Miami University and Apple and University of International Business and Economics
• Keywords: dimension folding; partial folding subspaces

Abstract

For complex matrix-valued data, dimension folding methods effectively perform sufficient dimension reduction while preserving the inner structure of data. The methods work well if the predictors are continuous. In this project, we study dimension folding problems with categorical variables. The categorical variable information is incorporated into dimension folding for regression and classification. The concepts of marginal, conditional, and partial folding subspaces are introduced, and their connections to the central folding subspaces are investigated. Estimation of the desired partial folding subspace, as well as the algorithm to estimate the structural dimensions are proposed. Simulations and real data analysis are included to evaluate the performance of the proposed method.