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    Sparse reduced-rank regression with covariance estimation

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    Type
    Article
    Authors
    Chen, Lisha
    Huang, Jianhua Z.
    KAUST Grant Number
    KUS-CI-016-04
    GRP-CF-2011-19-P-Gao-Huang
    Date
    2014-12-09
    Online Publication Date
    2014-12-09
    Print Publication Date
    2016-01
    Permanent link to this record
    http://hdl.handle.net/10754/623594
    
    Metadata
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    Abstract
    Improving the predicting performance of the multiple response regression compared with separate linear regressions is a challenging question. On the one hand, it is desirable to seek model parsimony when facing a large number of parameters. On the other hand, for certain applications it is necessary to take into account the general covariance structure for the errors of the regression model. We assume a reduced-rank regression model and work with the likelihood function with general error covariance to achieve both objectives. In addition we propose to select relevant variables for reduced-rank regression by using a sparsity-inducing penalty, and to estimate the error covariance matrix simultaneously by using a similar penalty on the precision matrix. We develop a numerical algorithm to solve the penalized regression problem. In a simulation study and real data analysis, the new method is compared with two recent methods for multivariate regression and exhibits competitive performance in prediction and variable selection.
    Citation
    Chen L, Huang JZ (2014) Sparse reduced-rank regression with covariance estimation. Statistics and Computing 26: 461–470. Available: http://dx.doi.org/10.1007/s11222-014-9517-6.
    Sponsors
    Huang’s work was partially supported by NSF grant DMS-1208952 and by Award Numbers KUS-CI-016-04 and GRP-CF-2011-19-P-Gao-Huang, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Springer Nature
    Journal
    Statistics and Computing
    DOI
    10.1007/s11222-014-9517-6
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11222-014-9517-6
    Scopus Count
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