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<p>In this paper, we focus on parameter estimation for sparse, correlated, high-dimensional linear regression models, and propose a framework to approximate a class of the oracle biased estimators. We term this approach the bias-enhanced support detection and root finding approach (BESDAR). The BESDAR algorithm significantly reduces estimation mean square error while improving predictive accuracy, and simultaneously lowers computational costs and iteration requirements. Under some certain conditions, we demonstrate that the BESDAR algorithm achieves sharp error bounds and obtain an optimal order within finite iterations. If the target signal is above the detectable level, the BESDAR algorithm will achieve the oracle biased estimator with high probability. Furthermore, we derive some classical biased estimators that satisfy our framework, such as the Ridge estimator, the Liu estimator. To overcome the over-compression of Ridge estimator and Liu estimator, we further propose the adaptive Liu estimator and adaptive Ridge estimator. Simulations and real data show that our proposed BESDAR algorithm outperforms some existing methods for variable selection when dealing with correlated data.</p>

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Bias-enhanced support detection and root finding approach

  • 期刊论文

  • 发表日期：

    2025年8月2日

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  • Hao Ming,
  • Hu Yang

摘要

In this paper, we focus on parameter estimation for sparse, correlated, high-dimensional linear regression models, and propose a framework to approximate a class of the oracle biased estimators. We term this approach the bias-enhanced support detection and root finding approach (BESDAR). The BESDAR algorithm significantly reduces estimation mean square error while improving predictive accuracy, and simultaneously lowers computational costs and iteration requirements. Under some certain conditions, we demonstrate that the BESDAR algorithm achieves sharp error bounds and obtain an optimal order within finite iterations. If the target signal is above the detectable level, the BESDAR algorithm will achieve the oracle biased estimator with high probability. Furthermore, we derive some classical biased estimators that satisfy our framework, such as the Ridge estimator, the Liu estimator. To overcome the over-compression of Ridge estimator and Liu estimator, we further propose the adaptive Liu estimator and adaptive Ridge estimator. Simulations and real data show that our proposed BESDAR algorithm outperforms some existing methods for variable selection when dealing with correlated data.