基于高维非稀疏条件偏相关系数的估计研究
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Estimation Study of Partial Correlation Coefficients Based on High-dimensional Non-sparse Conditions
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    目的 针对不同偏相关系数的估计方法,提出在高维非稀疏条件下不同偏相关系数估计方法的算法性能、估 计准确性和效率的探讨方法。 方法 现有 Pcor 估计方法的研究主要关注高维数据和稀疏性假设下偏相关关系的存 在性, 但是, 在非稀疏条件下,Pcor 估计方法的算法效率和估计准确性研究较为缺乏。 本研究综合考虑了适用于 非稀疏条件的偏相关系数估计方法, 并采用正则化方法处理相应的高维回归模型, 进一步探索估计方法对偏相关 系数的估计性能和效率,为验证不同算法的估计表现, 进行了大量的数值模拟实验, 并分析了股票市场中的实际 数据。 结果 在高维非稀疏条件下, 无偏自适应 LASSO 和渐进无偏 MCP 在偏相关系数的估计中表现都很出色。 结论 在高维非稀疏条件下, 偏相关系数的估计方法与高维稀疏条件下呈现出相似的特点: 当 Pcor 为负值时, 估 计较为准确; 当 Pcor 为正值时, 估计存在一定的偏差。 在正则化方法的选择上, 无偏自适应 LASSO 和渐进无偏 的 MCP 方法综合表现都优于相应的有偏 LASSO 方法,特别地, 在小样本量下, 自适应 LASSO·RES 算法表现较 优, 而在大样本量下, MCP·REG2 较好, 其中, REG2 方法在 Pcor 取正值时效果最好。 值得注意的是, 相较于稀 疏条件下控制变量得到有效控制, 在非稀疏条件下控制变量的干扰和影响增多,因此当非稀疏条件越趋近于稀疏 条件时, 算法误差越低, 效率越高;在适当的非稀疏性条件下, 无偏自适应 LASSO·RES 和渐进无偏 MCP·REG2 算法都表现良好, 也有较好的鲁棒性和稳定性;在较强非稀疏性条件下自适应 LASSO·RF 算法表现最好。

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    Objective This study explores algorithm performance estimation accuracy and efficiency of different partial correlation coefficient estimation methods under high-dimensional non-sparse conditions. Methods Existing research on Pcor estimation methods primarily focuses on the existence of partial correlation relationships in high-dimensional data under sparse assumptions. However research on algorithm efficiency and estimation accuracy of Pcor estimation methods under non-sparse conditions is relatively lacking. This study first comprehensively considered partial correlation coefficient estimation methods applicable to non-sparse conditions and employed regularization methods to handle corresponding high- dimensional regression models. Further exploration was conducted to investigate the estimation methods?? performance and efficiency regarding partial correlation coefficients. To verify the estimation performance of different algorithms extensive numerical simulation experiments were conducted and real data from the stock market were analyzed. Results Under high-dimensional non-sparse conditions both unbiased adaptive LASSO and asymptotically unbiased MCP performed excellently in estimating partial correlation coefficients. Conclusion Under high-dimensional non-sparse conditions partial correlation coefficient estimation methods exhibit similar characteristics to those under high-dimensional sparse conditions accurate estimation when Pcor is negative and some bias when Pcor is positive. In terms of regularization method selection the comprehensive performance of unbiased adaptive LASSO and asymptotically unbiased MCP methods is superior to the corresponding biased LASSO methods. Specifically under small sample sizes the performance of the adaptive LASSO·RES algorithm is superior while under large sample sizes MCP·REG2 performs better with REG2 being most effective when Pcor is positive. It is worth noting that controlling variables is more challenging and impactful under non-sparse conditions while controlling variables are effectively controlled under sparse conditions. Therefore as non-sparse conditions approach sparse conditions algorithmic errors decrease and efficiency increases. Under appropriate non-sparse conditions unbiased adaptive LASSO · RES and asymptotically unbiased MCP · REG2 algorithm perform well exhibiting good robustness and stability. Under stronger non-sparse conditions the adaptive LASSO·RF algorithm performs the best.

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杨静颖 ,晏 梅.基于高维非稀疏条件偏相关系数的估计研究[J].重庆工商大学学报(自然科学版),2025,42(3):118-126
YANG Jingying, YAN Mei. Estimation Study of Partial Correlation Coefficients Based on High-dimensional Non-sparse Conditions[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),2025,42(3):118-126

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  • 在线发布日期: 2025-05-14
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