Model Selection in High-Dimensional Linear Regression using Boosting with Multiple Testing
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结合提升与多重检验的高维线性回归模型选择
- 研究问题
- 在高维回归且解释变量高度共线时，如何筛选真实信号、抑制噪声与代理变量，并获得可靠的模型选择、系数估计及预测表现？
- 方法与思路
- 作者提出 BMT，将前向逐步选择与族错误率多重检验结合，每步只加入条件下最显著的变量，并利用强混合过程概率不等式分析性质。
- 材料陈述的贡献
- 摘要称，BMT 对保留真实信号并排除纯噪声的逼近模型具有 oracle 型性质；附加条件下可恢复真实模型，模拟与应用显示较好表现。
- 阅读关注点
- 应核对信号、代理与纯噪声的定义、多重检验阈值和停止规则、依赖及维度增长条件，以及逼近模型选择与真实模型恢复的区别。
- 阅读边界
- 所给来源为 arXiv 预印本，同行评审或期刊接收未获核实；摘要未列明完整条件与比较数值，不能据模拟陈述认定 BMT 普遍优于其他方法。
原文摘要
High-dimensional regression specification and analysis is a complex and active area of research in statistics, machine learning, and econometrics. This paper proposes a new approach, Boosting with Multiple Testing (BMT), which combines forward stepwise variable selection with the multiple testing framework of Chudik et al (2018). At each stage, the model is updated by adding only the most significant regressor conditional on those already included, while a family-wise multiple testing filter is applied to the remaining candidates. In this way, the method retains the strong screening properties of Chudik et al (2018) while operating in a less greedy manner with respect to proxy and noise variables. Using sharp probability inequalities for heterogeneous strongly mixing processes from Dendramis et al (2022), we show that BMT enjoys oracle type properties relative to an approximating model that includes all true signals and excludes pure noise variables: this model is selected with probability tending to one, and the resulting estimator achieves standard parametric rates for prediction error and coefficient estimation. Additional results establish conditions under which BMT recovers the exact true model and avoids selection of proxy signals. Monte Carlo experiments indicate that BMT performs very well relative to OCMT and Lasso type procedures, delivering higher model selection accuracy and smaller RMSE for the estimated coefficients, especially under strong multicollinearity of the regressors. Two empirical illustrations based on a large set of macro-financial indicators as covariates, show that BMT yields sparse, interpretable specifications with favourable out-of-sample performance.