Efficient variable selection for high-dimensional multiplicative models: a novel LPRE-based approach

This paper explores a novel high-dimensional sparse multiplicative model, which deal with data with positive responses, particularly in economical and biomedical researches. The proposed regularized method is conducted on the least product relative error (LPRE), and can be applied on various penalties including adaptive Lasso, SCAD, and MCP. An adjusted ADMM algorithm is adopted to obtain the estimators based on LPRE loss. Additionally, we prove the consistency and compute the convergence rates of the estimator. To validate the effectiveness of the proposed method, we conduct extensive numerical studies and real data analysis, yielding valuable insights and practical applications, utilizing well-known datasets of the Boston housing data and gold price data.