Model Selection: Generalized Lagrange Optimization Approach

Model selection is an important research direction in modern statistics, and the variable selection is the core problem of the model selection. When we are doing variable selection, we usually introduce more dependent variables related or may be related to the regression equation. The result is some minimal impact or no effect on the dependent variable are also included in the regression equation. Too many variables would increase the calculation, and decrease the accuracy of parameter estimates in the regression model. The literature has studied a number of model selection criteria, and the Lagrange optimization approach is preferable to the existing criteria under some assumptions. In this paper we will generalized the Lagrange optimization approach and prove it's asymptotic properties. Finally, we use numerical simulation to illustrate the good performance of the generalized criteria.