Choice Among Hypotheses Using Estimation Criteria

A rule for choosing among nested models is presented, taking into account that the usual model selection procedure is a sequence of tests, followed by estimation of the parameters that remain in the model. We take a decision theoretical approach and formulate the loss functions and the rules from a Bayesian point of view. The rule resembles a Neyman-Pearson type test but it takes into consideration the estimation loss across different candidate models and reports an estimate together with an associated loss, taking into account the uncertainty in the selection. The method is compared with other existing procedures and illustrated by examples.