Information-based inference for singular models and finite sample sizes: A frequentist information criterion

In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the predictive complexity. In the large-sample-size limit of a regular model, the predictive performance is well estimated by the Akaike Information Criterion (AIC). However, this approximation can either significantly under or over-estimating the complexity in a wide range of important applications where models are either non-regular or finite-sample-size corrections are significant. We introduce an improved approximation for the complexity that is used to define a new information criterion: the Frequentist Information Criterion (QIC). QIC extends the applicability of information-based inference to the finite-sample-size regime of regular models and to singular models. We demonstrate the power and the comparative advantage of QIC in a number of example analyses.Comment: 30 Pages, 6 figure