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.

翻译：许多实际医学问题中的数据往往同时具备稀疏与非稀疏结构。传统以促进稀疏性为主要目标的惩罚正则化技术，在此类情境下难以捕捉最优解。针对这些挑战，本文提出了一种名为非稀疏迭代（NSI）的新型算法。该算法允许稀疏与非稀疏结构并存，并能够同步且精确地对其进行估计。我们从理论上证明了所提算法收敛于Oracle解，并达到了$l_2$范数误差上界的最优速率。通过模拟实验与实际应用，与现有多种方法相比，NSI在估计精度、预测效能和变量选择方面均展现出卓越的统计性能。此外，该方法被应用于乳腺癌数据研究，揭示了对特定基因的重复筛选，为深入分析提供了依据。