Neural Network Model Selection Using Asymptotic Jackknife Estimator and Cross-Validation Method

Two theorems and a lemma are presented about the use of jackknife estimator and the cross-validation method for model selection. Theorem 1 gives the asymptotic form for the jackknife estimator. Combined with the model selection criterion, this asymptotic form can be used to obtain the fit of a model. The model selection criterion we used is the negative of the average predictive likelihood, the choice of which is based on the idea of the cross- validation method. Lemma 1 provides a formula for further exploration of the asymptotics of the model selection criterion. Theorem 2 given an asymptotic form of the model selection criterion for the regression case, when the parameters optimization criterion has a penalty term. Theorem 2 also proves the asymptotic equivalence of Moodys model selection criterion Moody, 1992 and the cross- validation method, when the distance measure between response y and regression function takes the form of a squared difference.... Neural networks, Model selection, Jackknife, Cross-validation.