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A0269
Title: Covariate information matrix for dimension reduction Authors:  Weixin Yao - UC Riverside (United States) [presenting]
Debmalya Nandy - The Pennsylvania State University (United States)
Bruce Lindsay - The Pennsylvania State University (United States)
Francesca Chiaromonte - The Pennsylvania State University (United States)
Abstract: Starting from the Density Information Matrix (DIM) approach, we develop a tool for Sufficient Dimension Reduction (SDR) in regression problems called Covariate Information Matrix (CIM). CIM exhaustively identifies the Central Subspace (CS) and provides a rank ordering of the reduced covariates in terms of their regression information. Compared to other popular SDR methods, CIM does not require distributional assumptions on the covariates, or estimation of the mean regression function. CIM is implemented via eigen-decomposition of a matrix estimated with the f2 method of computation, an efficient nonparametric density estimation technique. Expanding previous work, we also propose a bootstrap-based diagnostic tool for estimating the dimension of the CS. We use simulations and real data to demonstrate the effectiveness of our approach compared to other SDR methods.