  In fraud detection applications, the investigator is typically limited to
controlling a restricted number k of cases. The most efficient manner of
allocating the resources is then to try selecting the k cases with the highest
probability of being fraudulent. The prediction model used for this purpose
must normally be regularized to avoid overfitting and consequently bad
prediction performance. A new loss function, denoted the fraud loss, is
proposed for selecting the model complexity via a tuning parameter. A
simulation study is performed to find the optimal settings for validation.
Further, the performance of the proposed procedure is compared to the most
relevant competing procedure, based on the area under the receiver operating
characteristic curve (AUC), in a set of simulations, as well as on a VAT fraud
dataset. In most cases, choosing the complexity of the model according to the
fraud loss, gave a better than, or comparable performance to the AUC in terms
of the fraud loss.
