公司统金23级本科生郑乐轩在杨玥含教授指导下，在公司2A期刊同时也是统计学1区期刊Statistics and Computing发表了一篇关于包络模型的论文。本文提出提出工具变量包络模型IVE，将IV回归与包络降维统一起来，面向多元回归中常见的内生性问题。方法采用双阶段双包络：先基于工具变量构建X-envelope，对预测变量做IV调整以消除未观测混杂带来的偏差；再在变换后的设计上估计Y-envelope，剔除响应中的无关变异以提升效率。理论上证明IVE在内生性存在时仍无偏，并在一定条件下具有严格更小的渐近方差。仿真在低维与高维、相关预测变量等多种场景下表现稳健，预测误差优于传统包络与2SLS；汽车市场份额应用进一步验证其实际优势。

论文题目：Instrumental variable envelope models for endogenous multivariate regression

论文摘要：Envelope models are powerful tools for improving estimation efficiency in multivariate regression by identifying and excluding immaterial variation. However, existing envelope approaches typically rely on the assumption of exogenous predictors and thus fail to account for endogeneity arising from unobserved confounding. This paper introduces a novel framework that integrates instrumental variable (IV) techniques into envelope modeling, referred to as the Instrumental Variable Envelope (IVE) method. By unifying IV regression with dual-envelope dimension reduction, the IVE framework extends envelope methodology to accommodate endogenous regressors and high-dimensional covariates. The proposed two-stage procedure first constructs an IV-adjusted predictor envelope to eliminate confounding bias, and then estimates a response envelope on the transformed design. We establish the unbiasedness and asymptotic efficiency of the proposed estimator, and show that it achieves strictly lower variance than standard envelope estimators in the presence of endogeneity. Simulation studies confirm the superior predictive accuracy and robustness of the IVE method across a range of data-generating scenarios. An empirical application to automobile market share analysis further demonstrates the practical advantages of the proposed approach.

作者介绍：

杨玥含，William希尔官网入口教授，博导，北京大学博士。William希尔官网入口青年英才、龙马学者青年学者。主要从事因果推断、迁移学习等研究。在JASA、Biometrika、JBES、Pattern Recognition、《中国科学：数学》等国内外期刊发表论文40余篇。

郑乐轩，来自William希尔官网入口统计学-金融学双学位23，曾获国家奖学金，全面发展奖学金，学术科研与创新优秀奖学金，获得全国老员工数学竞赛国家二等奖，统计建模大赛北京市一等奖，正大杯国家三等奖

撰稿人：杨玥含

审稿人：邓 露