报告摘要：
In this article, we introduce a covariance-mean regression model with heterogeneous similarity matrices. It not only links the covariance of responses to heterogeneous similarity matrices induced by auxiliary information, but also establishes the relationship between the mean of responses and covariates. Under this new model setting, however, two statistical inference challenges are encountered. The first challenge is that the consistency of the covariance estimator based on the standard profile likelihood approach breaks down. Hence, we propose an adjustment and develop the Z-estimation and unconstrained/constrained ordinary least squares estimation methods. We demonstrate that the resulting estimators are consistent and asymptotically normal. The second challenge is testing the adequacy of the covariance-mean regression model comprising both the multivariate mean regression and the heterogeneous covariance matrices. Correspondingly, we introduce two diagnostic test statistics and then obtain their theoretical properties. The proposed estimators and tests are illustrated via extensive simulations and an empirical example study of the stock return comovement in the US stock market.This is a joint work with Wei Lan, Runze Li, and Chih-Ling Tsai.

个人简介：
邹韬博士，澳大利亚国立大学（Australian National University, ANU）金融精算与统计学院高级讲师（Senior Lecturer）、统计学本科项目主管。2011年在北京大学光华管理学院获得金融学学士，2012年在北京大学数学科学学院获得统计学双学士，2016年在北京大学光华管理学院获得统计学博士。邹韬博士的主要研究领域是协方差回归分析以及网络数据、金融数据、环境数据等相关数据和大数据建模。邹韬博士已经在统计学和计量经济学知名期刊Journal of the American Statistical Association, Journal of Econometrics, Journal of Business and Economic Statistics, Statistica Sinica 等发表多篇论文，并完成了Handbook of Financial Econometrics, Mathematics, Statistics, and Machine Learning 第113章的撰写工作。在教学领域，邹韬博士曾获得澳大利亚国立大学2020教学奖（ANU Vice-Chancellor’s Citation for Outstanding Contribution to Student Learning, 2020）以及商学院2019教学奖（College of Business and Economics Teaching Award for Outstanding Contribution to Student Learning, 2019）。