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Numerous practical medical problems often involve data that possess acombination of both sparse and non-sparse structures. Traditional penalizedregularizations techniques, primarily designed for promoting sparsity, areinadequate to capture the optimal solutions in such scenarios. To address thesechallenges, this paper introduces a novel algorithm named Non-sparse Iteration(NSI). The NSI algorithm allows for the existence of both sparse and non-sparsestructures and estimates them simultaneously and accurately. We providetheoretical guarantees that the proposed algorithm converges to the oraclesolution and achieves the optimal rate for the upper bound of the $l_2$-normerror. Through simulations and practical applications, NSI consistentlyexhibits superior statistical performance in terms of estimation accuracy,prediction efficacy, and variable selection compared to several existingmethods. The proposed method is also applied to breast cancer data, revealingrepeated selection of specific genes for in-depth analysis.

An iterative algorithm for high-dimensional linear models with both sparse and non-sparse structures