Joint variable and rank selection for parsimonious estimation of high-dimensional matrices

@article{Bunea2011JointVA,
  title={Joint variable and rank selection for parsimonious estimation of high-dimensional matrices},
  author={Florentina Bunea and Yiyuan She and Marten H. Wegkamp},
  journal={Annals of Statistics},
  year={2011},
  volume={40},
  pages={2359-2388}
}
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor selection and rank reduction are the most popular strategies for obtaining lower-dimensional approximations of the parameter matrix in such models. We show in this article that important gains in prediction accuracy can be obtained by considering them jointly… 

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