Following the work of Hurvich, Shumway, and Tsai (1990), we propose an “improved” variant of the Akaike information criterion, AICi, for state-space model selection. The variant is based on Akaike’s (1973) objective of estimating the Kullback-Leibler information (Kullback 1968) between the densities corresponding to the fitted model and the generating or true model. The development of AICi proc...

In linear mixed models, the Akaike information criterion (AIC) is often used to decide on the inclusion of a random effect. An important special case is the choice between linear and nonparametric regression models estimated using mixed model penalized splines. We investigate the behavior of two commonly used versions of the AIC, derived either from the implied marginal model or the conditional...

Akaike’s criterion is often used to test composite hypotheses; for example to determine the order of a priori unknown Auto-Regressive and/or Moving Average models. Objections are formulated against Akaike’s criterion and some modifications are proposed. The application of the theory leads to a general technique for AR-model order estimation based on testing pairs of composite hypotheses. This t...

The Akaike Information Criterion can be a valuable tool of scientific inference. This statistic, or any other statistical method for that matter, cannot, however, be the whole of scientific methodology. In this paper some of the limitations of Akaikean statistical methods are discussed. It is argued that the full import of empirical evidence is realized only by adopting a richer ideal of empiri...

In linear mixed models, the conditional Akaike Information Criterion (cAIC) is a procedure for variable selection in light of the prediction of specific clusters or random effects. This is useful in problems involving prediction of random effects such as small area estimation, and much attention has been received since suggested by Vaida and Blanchard (2005). A weak point of cAIC is that it is ...