Consistent Bayesian information criterion based on a mixture prior for possibly high‐dimensional multivariate linear regression models
该研究为多元线性回归模型中的变量选择问题提出了新的贝叶斯信息准则，融合了AIC和BIC的优点，在大样本和高维框架下均能一致地选择真实变量集，模拟实验显示其高概率选对变量。
Abstract In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Inheriting their asymptotic properties, our information criteria are consistent in variable selection in both the large‐sample and the high‐dimensional asymptotic frameworks. In numerical simulations, variable selection methods based on our information criteria choose the true set of variables with high probability in most cases.