Density ratio model selection

Abstract

The density ratio model presumes that the log-likelihood ratio of two unknown densities is of some known parametric linear form. However, the choice of the functional form has an impact on both estimation and testing. The problem of over/underfitting in the context of the density ratio model is examined and the theory shows that bias and loss of efficiency are introduced when the model is misspecified. The problem of identifying the appropriate functional form for an application of the density ratio model is addressed by means of model selection criteria, which perform reasonably well. Several simulations integrate the presentation.