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Complex distributions of the healthcare expenditure pose challenges tostatistical modeling via a single model. Super learning, an ensemble methodthat combines a range of candidate models, is a promising alternative for costestimation and has shown benefits over a single model. However, standardapproaches to super learning may have poor performance in settings whereextreme values are present, such as healthcare expenditure data. We propose asuper learner based on the Huber loss, a "robust" loss function that combinessquared error loss with absolute loss to down-weight the influence of outliers.We derive oracle inequalities that establish bounds on the finite-sample andasymptotic performance of the method. We show that the proposed method can beused both directly to optimize Huber risk, as well as in finite-sample settingswhere optimizing mean squared error is the ultimate goal. For this latterscenario, we provide two methods for performing a grid search for values of therobustification parameter indexing the Huber loss. Simulations and real dataanalysis demonstrate appreciable finite-sample gains in cost prediction andcausal effect estimation using our proposed method.

A Huber loss-based super learner with applications to healthcare expenditures