Optimal model assessment, selection, and combination

Central to statistical theory and application is statistical modeling, which typically involves choosing a single model or combining a number of models of different sizes and from different sources. Whereas model selection seeks a single best modeling procedure, model combination combines the strength of different modeling procedures. In this article we look at several key issues and argue that model assessment is the key to model selection and combination. Most important, we introduce a general technique of optimal model assessment based on data perturbation, thus yielding optimal selection, in particular model selection and combination. From a frequentist perspective, we advocate model combination over a selected subset of modeling procedures, because it controls bias while reducing variability, hence yielding better performance in terms of the accuracy of estimation and prediction. To realize the potential of model combination, we develop methodologies for determining the optimal tuning parameter, such as weights and subsets for combining via optimal model assessment. We present simulated and real data examples to illustrate main aspects.