PARAMETER-BASED HYPOTHESIS TESTS FOR MODEL SELECTION

This paper explores parameter-based hypothesis tests for selecting between candidate models that predict an unknown variable from observations. 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 penalty. Hypothesis tests are proposed for assessing the statistical evidence for parameters taking non-zero values. These compare closely with standard criteria such as Akaike's and the Bayesian information criterion. 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.