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.jpg): Failed to open stream: No such file or directory in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 117 J+Multivar+Anal
2017 ; 157
(ä): 14-28
Nephropedia Template TP
J Multivar Anal
2017[May]; 157
(ä): 14-28
PMID28989203
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Many modern statistical problems can be cast in the framework of multivariate
regression, where the main task is to make statistical inference for a possibly
sparse and low-rank coefficient matrix. The low-rank structure in the coefficient
matrix is of intrinsic multivariate nature, which, when combined with sparsity,
can further lift dimension reduction, conduct variable selection, and facilitate
model interpretation. Using a Bayesian approach, we develop a unified sparse and
low-rank multivariate regression method to both estimate the coefficient matrix
and obtain its credible region for making inference. The newly developed sparse
and low-rank prior for the coefficient matrix enables rank reduction, predictor
selection and response selection simultaneously. We utilize the marginal
likelihood to determine the regularization hyperparameter, so our method
maximizes its posterior probability given the data. For theoretical aspect, the
posterior consistency is established to discuss an asymptotic behavior of the
proposed method. The efficacy of the proposed approach is demonstrated via
simulation studies and a real application on yeast cell cycle data.