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There are two type of model selection methods.One method is the best subset pro-cedure.The other one selects variables via various shrinkage methods.We propose a hybrid information criterion,with the well known minimax concave penalty as a special case.The hybrid information criterion combines the concave penalty criterion and best subset procedure.It essen-tially screens variables by the minimax concave penalty and selects the correct variables by the best subset procedure simultaneously.This new criterion connects the above two type of criteria.On the one hand,we can select variables via shrinkage method.On the other hand,we can select the correct tuning parameter by the best subset procedure.In addition,if we set the hybrid information criterion as a reference for model selection,we can show that γM = 2:7 for the minimax concave penalty is a robust choice.Thus,the essential connection between the minimax concave penalty and some best subset procedures is revealed.