A new sparse variable selection via random-effect model

We study a new approach to simultaneous variable selection and estimation via random-effect models. Introducing random effects as the solution of a regularization problem is a flexible paradigm and accommodates likelihood interpretation for variable selection. This approach leads to a new type of penalty, unbounded at the origin and provides an oracle estimator without requiring a stringent condition. The unbounded penalty greatly enhances the performance of variable selections, enabling highly accurate estimations, especially in sparse cases. Maximum likelihood estimation is effective in enabling sparse variable selection. We also study an adaptive penalty selection method to maintain a good prediction performance in cases where the variable selection is ineffective.