Abstract:
This article studies the estimation of the precision matrix of a high-dimensional Gaussian
network. We investigate the graphical selector operator with shrinkage, GSOS for short, to maximize
a penalized likelihood function where the elastic net-type penalty is considered as a combination of
a norm-one penalty and a targeted Frobenius norm penalty. Numerical illustrations demonstrate
that our proposed methodology is a competitive candidate for high-dimensional precision matrix
estimation compared to some existing alternatives. We demonstrate the relevance and efficiency of
GSOS using a foreign exchange markets dataset and estimate dependency networks for 32 different
currencies from 2018 to 2021.
