报 告 人：郭旭 教授

报告题目：High-dimensional inference for single-index model with latent factors

报告时间：2024年9月26日（星期四）下午4：00

报告地点：静远楼1506学术报告厅

主办单位：数学研究院、数学与统计学院、科学技术研究院

报告人简介：

       郭旭博士，北京师范大学统计学院教授，博士生导师，长期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。主持国家自然科学基金优秀青年项目、面上项目、青年项目各1项。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。  

报告摘要：

        Models with latent factors recently attract a lot of attention. However, most investigations focus on linear regression models and thus cannot capture nonlinearity. To address this issue, we propose a novel Factor Augmented Single-Index Model. 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. No moment condition for the error term is imposed for our proposal. Thus our procedures work well when random error follows heavy-tailed distributions or when outliers are present. We demonstrate the finite sample performance of the proposed method through comprehensive numerical studies and its application to an FRED-MD macroeconomics dataset.