Statistica Sinica 30 (2020), 1069-1094
Abstract: In this study, we employ the broken adaptive ridge method to estimate the lower-dimensional patterns of the coefficients in regression models. Based on a reweighted 𝓁2-penalization, the new method simultaneously recovers the true sparsity and the inherent structures of the features, making it theoretically and practically appealing. The resulting estimate is shown to enjoy the oracle property. The proposed method also contains a set of variable selection or pattern estimation methods. As a special case, the fused broken adaptive ridge, which penalizes the differences between adjacent coefficients, is thoroughly discussed, with applications to signal approximation and image processing. The associated algorithms are numerically easy to implement. Simulation studies and real-data analyses illustrate the advantages of the proposed method over the fused lasso method.
Key words and phrases: Linear regression, oracle estimator, re-weighted 𝓁2-penalization.