Estimation When Both Covariance and Precision Matrices are Sparse

@article{MacNamara2021EstimationWB,
  title={Estimation When Both Covariance and Precision Matrices are Sparse},
  author={Shev MacNamara and Erik Schl{\"o}gl and Zdravko I. Botev},
  journal={2021 Winter Simulation Conference (WSC)},
  year={2021},
  pages={1-11}
}
We offer a method to estimate a covariance matrix in the special case that both the covariance matrix and the precision matrix are sparse - a constraint we call double sparsity. The estimation method is maximum likelihood, subject to the double sparsity constraint. In our method, only a particular class of sparsity pattern is allowed: both the matrix and its inverse must be subordinate to the same chordal graph. Compared to a naive enforcement of double sparsity, our chordal graph approach… 
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Robust sparse precision matrix estimation for high-dimensional compositional data

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