A sparse estimation technique for general model structures

In this paper, a general sparse estimator is proposed, based on the maximum likelihood / prediction error method (or any √N-consistent estimator). This procedure does not rely on the convexity of the cost function of the underlying estimator (in case such estimator is an M-estimator), and it provides an automatic tuning of the (implicit) regularization parameter. The idea behind the proposed method is a three step procedure, where the first step consists in a standard √N-consistent estimation, the second step seeks for the sparsest estimate in a neighborhood of the initial estimate, and the last step is a refinement based on the sparseness pattern estimated in the second step. A rigorous statistical analysis is provided, which establishes conditions for consistency, asymptotic variable selection and the so-called Oracle property. A simulation example is given to demonstrate the performance of the method.