  This paper aims to better predict highly skewed auto insurance claims by
combining candidate predictions. We analyze a version of the Kangaroo Auto
Insurance company data and study the effects of combining different methods
using five measures of prediction accuracy. The results show the following.
First, when there is an outstanding (in terms of Gini Index) prediction among
the candidates, the "forecast combination puzzle" phenomenon disappears. The
simple average method performs much worse than the more sophisticated model
combination methods, indicating that combining different methods could help us
avoid performance degradation. Second, the choice of the prediction accuracy
measure is crucial in defining the best candidate prediction for "low frequency
and high severity" (LFHS) data. For example, mean square error (MSE) does not
distinguish well between model combination methods, as the values are close.
Third, the performances of different model combination methods can differ
drastically. We propose using a new model combination method, named
ARM-Tweedie, for such LFHS data; it benefits from an optimal rate of
convergence and exhibits a desirable performance in several measures for the
Kangaroo data. Fourth, overall, model combination methods improve the
prediction accuracy for auto insurance claim costs. In particular, Adaptive
Regression by Mixing (ARM), ARM-Tweedie, and constrained Linear Regression can
improve forecast performance when there are only weak learners or when no
dominant learner exists.
