  Numerous practical medical problems often involve data that possess a
combination of both sparse and non-sparse structures. Traditional penalized
regularizations techniques, primarily designed for promoting sparsity, are
inadequate to capture the optimal solutions in such scenarios. To address these
challenges, this paper introduces a novel algorithm named Non-sparse Iteration
(NSI). The NSI algorithm allows for the existence of both sparse and non-sparse
structures and estimates them simultaneously and accurately. We provide
theoretical guarantees that the proposed algorithm converges to the oracle
solution and achieves the optimal rate for the upper bound of the $l_2$-norm
error. Through simulations and practical applications, NSI consistently
exhibits superior statistical performance in terms of estimation accuracy,
prediction efficacy, and variable selection compared to several existing
methods. The proposed method is also applied to breast cancer data, revealing
repeated selection of specific genes for in-depth analysis.
