2020年12月15日下午5点30分，东北师范大学冯龙副教授莅临我院做学术报告，在南湖校区教学科研楼412室，东北师范大学刘秉辉教授莅临我院做学术报告，会议由数学与统计学院副院长徐平峰主持，学院部分老师、研究生参加了本次学术报告会。

报告题目：Max-Sum tests for cross-sectional dependence of high-dimensional panel data

摘要：We consider a testing problem for cross-sectional dependence for high-dimensional panel data, where the number of cross-sectional units is potentially much larger than the number of observations. The cross-sectional dependence is described through a linear regression model. We study three tests named the sum test, the max test and the max-sum test, where the latter two are new. The sum test is initially proposed by Breusch and Pagan (1980). We design the max and sum tests for sparse and non-sparse residuals in the linear regressions, respectively. And the max-sum test is devised to compromise both situations on the residuals. Indeed, our simulation shows that the max-sum test outperforms the previous two tests. This makes the max-sum test very useful in practice where sparsity or not for a set of data is usually vague. Towards the theoretical analysis of the three tests, we have settled two conjectures regarding the sum of squares of sample correlation coefficients asked by Pesaran (2004 and 2008). In addition, we establish the asymptotic theory for maxima of sample correlations coefficients appeared in the linear regression model for panel data, which is also the first successful attempt to our knowledge. To study the max-sum test, we create a novel method to show asymptotic independence between maxima and sums of dependent random variables. We expect the method itself is useful for other problems of this nature. Finally, an extensive simulation study as well as a case study are carried out. They demonstrate advantages of our proposed methods in terms of both empirical powers and robustness for residuals regardless of sparsity or not.

冯龙简介：东北师范大学数学与统计学院副教授。博士毕业于南开大学。在国际高水平杂志JASA, AOS, Biometrika等发表SCI论文20篇。主持一项国家自然科学基金青年项目。

在报告中，冯副教授首先向我们细致深刻的分析了一个高维面板数据的横截面独立性测试问题，用线性回归模型描述了截面相关性。冯副教授向我们讲述了他研究的三个测试，即the sum test、the max test和the max-sum test，其中后两个是新的。报告中分别设计了线性回归中稀疏残差和非稀疏残差的最大和和检验，并设计了最大和检验来保证残差的两种情况。此外，冯副教授还建立了面板数据线性回归模型中样本相关系数极大值的渐近理论，这也是对高维数据这方面知识的首次成功尝试。最后，冯副教授进行了大量的仿真研究和案例研究。证明了冯副教授提出的方法在残差是否稀疏的情况下，经验能力和稳健性方面都具有优势。

报告结束后，参会人员踊跃提问，就感兴趣的问题向冯龙副教授进行讨论与交流，冯龙副教授就提出的问题进行了详细的解答，并分享了自己的心得。数学统计学院副院长徐平峰再次向冯龙副教授的到来表示诚挚的感谢。

本次学术交流会拓展了同学们的学术视野，也激发了同学们的学习热情，更加努力学习研究新的领域与方法，并使老师和同学们对分割似然有了更深的理解，聆听报告的师生均表示受益匪浅。

数学与统计学院

2020年12月15日