带有异质参数的高维线性回归模型的Model-X Knockoffs推断方法研究  

Research on Model-X Knockoffs Inference for High-Dimensional Linear Regression Model with Heterogeneous Parameters

作　　者：潘莹丽 夏迪 龙杰新 刘展 PAN Ying-li;XIA Di;LONG Jie-xin;LIU Zhan(Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China;Hubei Key Laboratory of Applied Mathematics,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学数学与统计学学院,湖北武汉430062 [2]应用数学湖北省重点实验室,湖北武汉430062

出　　处：《数理统计与管理》2025年第1期119-134,共16页Journal of Applied Statistics and Management

基　　金：国家社会科学基金青年项目(24CTJ004)。

摘　　要：大数据是传统软件工具在一定时间内无法捕获、管理和处理的数据集。它是一种海量、高增长率、多元化的信息资产,需要新的处理模式才能具有更强的决策权、洞察力和流程优化能力。大数据背景下,研究者面临着维数灾难和数据异质的困扰。在带有异质参数的高维线性回归模型下,本文通过构造Model-Xknockoffs变量实现变量选择中错误发现率(FDR)的控制;通过使用fusedlasso方法有效识别和合并同质参数组,并评估研究间的异质性。模拟和实证研究结果表明:将Model-Xknockoffs的推断方法和fusedlasso方法结合能有效解决带有异质参数的高维线性回归模型中参数估计、变量选择和FDR控制的问题。Big data is a set of data that cannot be captured,managed and processed by traditional software tools within a certain period of time.It is a massive,high-growth,diversified information asset that requires new processing models for greater decision power,insight,and process optimization.In the background of big data,researchers faced the problems of curse of dimensionality and data heterogeneity.In this paper,we construct Model-X knockoffs variables to control the false discovery rate(FDR)in variables selection of high-dimensional linear regression model with heterogeneous parameters.We propose the fused lasso method to availably identify and merge homogeneous parameters clusters,and evaluate inter-study heterogeneity.The simulation studies and real data analysis show that:the combination of Model-X knockoffs inference method and fused lasso method can solve accurately the problems of parameter estimation,variables selection and FDR control in high-dimensional linear regression model with heterogeneous parameters.

关 键 词：model-Xknockoffs FDR 异质性 fusedlasso 

分 类 号：O212[理学—概率论与数理统计]