Strong Consistency Of The Information Criteria For Multivariate Linear Regression Model Under The Large-dimensional Asymptotic Framework

The model selection methods is helpful for improving interpretation of the model in multivariate linear regression model.Although a number of criteria have been suggested,the most widely used are the classical model selection methods in practice,i.e.,AIC,BIC,Cp and extensions.Experience has shown that these classical model selection methods are not always suitable for high-dimensional condition,the and for selecting variables are inconsistent when the sample size is large,while the BIC,C AIC,AICc are consistent;However,when the the sample size and the dimension of the response variables are large,the and for selecting variables are consistent,but the BIC,C AIC,AICc are not.The methods of AIC,BIC,KIC,C AIC,AICc(they are collectively called AICs)are included in a family of information criteria defined by adding a negative twofold maximum log-likelihood to a penalty term expressing the complexity of the model.Each method is defined by different penalty items,the present paper examines the strong consistent properties of AICs under the large-dimension asymptotic framework.