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Activity Number: 80 - Sufficient Dimension Reduction and Applications
Type: Topic-Contributed
Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #317558
Title: Least Squares and Maximum Likelihood Estimation of Sufficient Reductions in Regressions with Matrix Valued Predictors
Author(s): Efstathia Bura* and Daniel Kapla and Ruth Pfeiffer
Companies: TU Wien and TU Wien and NCI-DCEG
Keywords:
Abstract:

We propose methods to estimate sufficient reductions of matrix-valued predictors for regression or classification. We assume that the first moment of the predictor matrix given the response can be decomposed into a row and column component via a Kronecker product structure. We obtain least squares and maximum likelihood estimates of the sufficient reductions of the matrix predictors, derive statistical properties of the resulting estimates and present fast computational algorithms with assured convergence. The performance of the proposed approaches in regression and classification is compared in simulations. We illustrate the methods on two examples, using longitudinally measured serum biomarker and neuroimaging data.


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