Generalized information criterion

In this article, we propose a generalized Akaike's information criterion (AIC) (GAIC), which includes the usual AIC as a special case, for general class of stochastic models (i.e. i.i.d., non-i.i.d., time series models etc.). Then we derive the asymptotic distribution of selected order by GAIC, and show that is inconsistent, i.e. (true order). This is the problem of selection by completely specified models. In practice, it is natural to suppose that the true model g would be incompletely specified by uncertain prior information, and be contiguous to a fundamental parametric model with dimθ ₀=p ₀. One plausible parametric description for g is , h=(h ₁,...,h _K-p ₀)′ where n is the sample size, and the true order is K. Under this setting, we derive the asymptotic distribution of Then it is shown that GAIC has admissible properties for perturbation of models with order of , where the length {norm of matrix}h{norm of matrix} is large. This observation seems important. Also numerical studies will be given to confirm the results.