PARAMETER-BASED HYPOTHESIS TESTS FOR MODEL SELECTION

This paper explores parameter-based hypothesis tests for selecting bet ween candidate models that predict an unknown variable from observatio ns. This is the form of many time series models, classifiers, and data -fitting models. The basis for this paper is that if a model contains redundant terms the associated parameters can be set to zero without p enalty. Hypothesis tests are proposed for assessing the statistical ev idence for parameters taking non-zero values. These compare closely wi th standard criteria such as Akaike's and the Bayesian information cri terion. A numerical simulation is presented to illustrate the criteria . The link between selection criteria based on parameter distributions and those based on data distributions is relevant to techniques such as changepoint methods. Resampling and other similar techniques may be applied using this framework.