Selection of an optimal penalty for proxy-likelihood model selection

Determine which model-selection penalty, particularly the composite likelihood AIC penalty or the standard AIC penalty, is better calibrated and more appropriate for selecting TLETS models with the Hüsler–Reiss composite proxy-likelihood.

Background

The paper compares composite likelihood AIC (CLAIC) with standard AIC when selecting among TLETS models. In the wildfire application, the two penalties select different models: CLAIC favors a higher-order transformed-linear moving-average model, whereas standard AIC favors a transformed-linear autoregressive moving-average model.

The authors note that the composite-likelihood penalties are small and may not be well calibrated, while standard AIC lacks the usual theoretical justification because the proxy-likelihood is not the correct likelihood. The relative suitability of the competing penalties therefore remains unresolved.