Model selection and estimation in the Gaussian graphical model. (English) Zbl 1142.62408

Yuan, Ming; Lin, Yi

Biometrika 94, No. 1, 19-35 (2007).

Summary: We propose penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model. The methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite, and thus conduct model selection and estimation simultaneously. The implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix, but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization. We propose a BIC-type criterion for the selection of the tuning parameter in the penalized likelihood methods. The connection between our methods and existing methods is illustrated. Simulations and real examples demonstrate the competitive performance of the new methods.

MSC:

62N02	Estimation in survival analysis and censored data
62P10	Applications of statistics to biology and medical sciences; meta analysis
65C60	Computational problems in statistics (MSC2010)

Keywords:

covariance selection; lasso; maxdet algorithm; nonnegative garrote; penalized likelihood