A constrained minimum criterion for variable selection
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For variable selection in the sparse linear model setting, we propose a new criterion which chooses the subset with the minimum number of variables under the constraint that the likelihood of the subset is above a certain level. When applied to the best subset selection, this criterion gives users direct control on the probability of choosing the correct subset in an asymptotic sense and a consistent estimator for the model parameter vector. It also has an interpretation as a likelihood-ratio test procedure for detecting the cardinality of the true model. When applied to the lasso, this criterion eliminates the need for selecting the lasso tuning parameter as it is automatically determined by the likelihood level in the criterion. Under mild conditions, the lasso estimator under this criterion is consistent. Simulation results show that this criterion gives the lasso better selection accuracy than the cross-validation criterion in many cases. The criterion also automatically gives the chosen model its level of significance which provides users more information for decision making.
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