Probabilities of overfitting of Model Selection Criteria in Regression

In this paper, we derived overfitted probabilities for model selection criteria in orthogonal regression for two different situations. First, there is one candidate model with one extra variable is compared to the current model. Second, we expanded to m candidate models. We assume that these comparisons are independent and discuss overfitting probabilities. We found the overfitting probabilities of AIC, AICc, SIC, SICc, and HQ on one extra variable case and multiple extra variable case.