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Least squares and maximum likelihood estimation of sufficient reductions in regressions with matrix-valued predictors
- Source :
- International Journal of Data Science and Analytics
- Publication Year :
- 2020
- Publisher :
- Springer International Publishing, 2020.
-
Abstract
- We propose methods to estimate sufficient reductions in 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 in 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.
- Subjects :
- Maximum likelihood
010103 numerical & computational mathematics
01 natural sciences
Least squares
Reduction (complexity)
010104 statistics & probability
symbols.namesake
Matrix (mathematics)
Statistics::Machine Learning
Dimension (vector space)
Statistics
Convergence (routing)
Regular Paper
Statistics::Methodology
0101 mathematics
Mathematics
Reduction
Kronecker product
Applied Mathematics
Classification
Regression
Computer Science Applications
Computational Theory and Mathematics
Modeling and Simulation
symbols
Dimension
Information Systems
Subjects
Details
- Language :
- English
- ISSN :
- 23644168 and 2364415X
- Volume :
- 11
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- International Journal of Data Science and Analytics
- Accession number :
- edsair.doi.dedup.....9dd0557f554b902c7014b29112f84718