Recovery of partly sparse and dense signals

Abstract

In high-dimensional data analysis, we often encounter partly sparse and dense signals or parameters. Considering an lq-penalization with different qs for each sub-vector of the signals, we formularize an optimal solution for q=1 or 2 in a linear regression model to well represent such signals or parameters. We also provide an algorithm to derive it. Furthermore, we provide the consistency result of the variable selection in this optimal solution under a fixed design. Simulation study and real-data analysis illustrate its improved variable selection performance relative to the conventional methods.