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Estimation of a sparse group of sparse vectors

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  • Felix Abramovich
  • Vadim Grinshtein

Abstract

We consider estimating a sparse group of sparse normal mean vectors, based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their significant components, which can be performed by a fast algorithm. The resulting estimators are developed within a Bayesian framework and can be viewed as maximum a posteriori estimators. We establish their adaptive minimaxity over a wide range of sparse and dense settings. A simulation study demonstrates the efficiency of the proposed approach, which successfully competes with the sparse group lasso estimator. Copyright 2013, Oxford University Press.

Suggested Citation

  • Felix Abramovich & Vadim Grinshtein, 2013. "Estimation of a sparse group of sparse vectors," Biometrika, Biometrika Trust, vol. 100(2), pages 355-370.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:355-370
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    File URL: http://hdl.handle.net/10.1093/biomet/ass082
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