重庆工商大学学报（自然科学版）2025，Vol.42Issue(3)：118-126,9.DOI:10.16055/j.issn.1672-058X.2025.0003.015
基于高维非稀疏条件偏相关系数的估计研究
Estimation Study of Partial Correlation Coefficients Based on High-dimensional Non-sparse Conditions
摘要
Abstract
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.关键词
偏相关系数/高维数据/非稀疏条件/正则化方法/LASSO/自适应LASSO/MCPKey words
partia correlation coefficient/high-dimensional data/non-sparse conditions/regularization methods/LASSO/adaptive LASSO/MCP分类
数理科学引用本文复制引用
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):118-126,9.基金项目
云南省科技计划基础研究项目(202201AU070051) （202201AU070051）
云南师范大学博士科研启动项目(2020ZB014) （2020ZB014）
云南省现代分析数学及其应用重点实验室(202302AN360007). （202302AN360007）
