Consistent Bayesian information criterion based on a mixture prior for possibly high‐dimensional multivariate linear regression models

In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on prior mixing smooth distribution and delta distribution. Each them can be interpreted as fusion Akaike criterion (AIC) (BIC). Inheriting their asymptotic properties, our are consistent variable selection both large-sample high-dimensional frameworks. numerical simulations, methods choose true set with high probability most cases.