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A constrained minimum method for model selection

We propose a constrained minimum method for converting a hypothesis test into a model selection criterion that pursues consistency and sparsity of the selected model explicitly. The method achieves consistency by letting the significance level of the test go to zero at a certain speed depending on the sample size. It maximizes the sparsity by choosing the most sparse model among models not rejected by the test. The method may be used for model selection whenever a hypothesis test on the model parameter vector is available. We illustrate this method through its application to the best subset selection of linear models. Numerical comparisons with existing methods show that it has excellent accuracy and its selected model converges to the true model faster than the model chosen by the Bayesian information criterion.