Estimation and inference of high-dimensional factor augmented regression model
Holder： Xu Guo（Beijing Normal University）
Time：2025-03-20 14:00-15:00
Location：Siyuan Lecture Hall，Zhi Hua Building-225
Abstract:
Factor model is a powerful tool to deal with high correlations among predictors. It has also been incorporated in regression analysis. In this talk, I will share recent developments about estimation and inference of high-dimensional factor augmented regression model. In particular, I will discuss high-dimensional semiparametric factor augmented regression model. Among others, single-index model and partially linear regression model are two widely investigated semiparametric models. However existing methods do not perform well when predictors are highly correlated. We first address the concern whether it is necessary to consider the augmented part by introducing a score-type test statistic. Compared with previous test statistics, our proposed test statistic does not need to estimate the high-dimensional regression coefficients, nor high-dimensional precision matrix, making it simpler in implementation. We also propose a Gaussian multiplier bootstrap to determine the critical value. The validity of our procedure is theoretically established under suitable conditions. We further investigate the penalized estimation of the regression model. With estimated latent factors, we establish the error bounds of the estimators. Lastly, we introduce debiased estimator and construct confidence interval for individual coefficient based on the asymptotic normality. Simulation studies and real data analysis are conducted to illustrate the proposed methods.
About the Speaker:
郭旭，现为北京师范大学统计学院教授，博士生导师。郭老师一直从事回归分析中复杂假设检验的理论方法及应用研究，近年来旨在对高维数据发展适当有效的检验方法。部分成果发表在JRSSB, JASA，Biometrika和JOE。现主持国家自然科学基金青年科学基金项目B类（原优秀青年科学基金）。曾荣获北师大第十一届“最受本科生欢迎的十佳教师”，北师大第十八届青教赛一等奖和北京市第十三届青教赛三等奖。
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