報 告 人：郭旭 教授

報告題目：High-dimensional inference for single-index model with latent factors

報告時間：2024年9月26日（星期四）下午4：00

報告地點：靜遠樓1506學術報告廳

主辦單位：數學研究院、數學與統計學院、科學技術研究院

報告人簡介：

       郭旭博士，北京師范大學統計學院教授，博士生導師，長期從事回歸分析中復雜假設檢驗的理論方法及應用研究，近年來旨在對高維數據發展適當有效的檢驗方法，部分成果發表在JRSSB, JASA，Biometrika和JOE。主持國家自然科學基金優秀青年項目、面上項目、青年項目各1項。曾榮獲北師大第十一屆“最受本科生歡迎的十佳教師”，北師大第十八屆青教賽一等獎和北京市第十三屆青教賽三等獎。  

報告摘要：

        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.