Tuning parameter selection information criteria

Provide information criteria for selecting tuning parameters.

Usage

criterion(hatOmega, S, n, crit, ebic.tuning = 0.5)

Arguments

hatOmega

The estimated precision matrix.

S

The sample covariance matrix.

n

An integer specifying the sample size.

crit

A string specifying the tuning parameter selection criterion to use. Available options include:

1. "AIC": Akaike information criterion (Akaike 1973) .

2. "BIC": Bayesian information criterion (Schwarz 1978) .

3. "EBIC": extended Bayesian information criterion (Foygel and Drton 2010) .

4. "HBIC": high dimensional Bayesian information criterion (Wang et al. 2013; Fan et al. 2017) .

ebic.tuning

A scalar (default = 0.5) specifying the tuning parameter to calculate for crit = "EBIC".

Value

A scalar.

References

Akaike H (1973). “Information Theory and an Extension of the Maximum Likelihood Principle.” In Petrov BN, Csáki F (eds.), Second International Symposium on Information Theory, 267–281. Akad\'emiai Kiad\'o, Budapest, Hungary.

Fan J, Liu H, Ning Y, Zou H (2017). “High Dimensional Semiparametric Latent Graphical Model for Mixed Data.” Journal of the Royal Statistical Society Series B: Statistical Methodology, 79(2), 405–421. doi:10.1111/rssb.12168 .

Foygel R, Drton M (2010). “Extended Bayesian Information Criteria for Gaussian Graphical Models.” In Lafferty J, Williams C, Shawe-Taylor J, Zemel R, Culotta A (eds.), Advances in Neural Information Processing Systems 23 (NIPS 2010), 604–612.

Schwarz G (1978). “Estimating the Dimension of a Model.” The Annals of Statistics, 6(2), 461–464. doi:10.1214/aos/1176344136 .

Wang L, Kim Y, Li R (2013). “Calibrating Nonconvex Penalized Regression in Ultra-High Dimension.” The Annals of Statistics, 41(5), 2505–2536. doi:10.1214/13-AOS1159 .