Significance Tests for Gaussian Graphical Models Based on Shrunken Densities

Gaussian Graphical Models (GGMs) are important probabilistic graphical models in Statistics. Inferring a GGM’s structure from data implies computing the inverse of the covariance matrix (i.e. the precision matrix). When the number of variables p is larger than the sample size n, the (sample) covariance estimator is not invertible and therefore another estimator is required. Covariance estimators based on shrinkage are more stable (and invertible), however, classical hypothesis testing for the ”shrunk” coefficients is an open challenge. In this paper, we present an exact null-density that naturally includes the shrinkage, and allows an accurate parametric significance test that is accurate and computationally efficient.