  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.
