The copula information criteria
Journal article, Peer reviewed
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- Scientific articles 
Original versionScandinavian Journal of Statistics, 41(2014)2: 436-459 10.1111/sjos.12042
We derive two types of Akaike information criterion (AIC)-like model-selection formulae for the semiparametric pseudo-maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation of a certain Kullback–Leibler information distance. This gives a significantly different formula compared with the AIC, which we name the copula information criterion. However, we show that such a model-selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. We then derive what we call the cross-validation copula information criterion, which exists under weak conditions and is a first-order approximation to exact cross validation. This formula is very similar to the standard AIC formula but has slightly different motivation. A brief illustration with real data is given.
This is the author’s accepted, refereed and final manuscript to the article.