主 题：Asymptotic theory for the quadratic assignment procedure二次分配程序的渐近理论

主讲人：加州大学伯克利分校石磊博士生

主持人：统计学院林华珍教授

时间：2024年12月26日（周四）下午4：00-5：00

线下地点：柳林校区弘远楼408会议室

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

Lei Shi is a Ph.D. student in Berkeley Biostatistics, advised by Professor Jingshen Wang and Professor Peng Ding. He works on causal inference and high dimensional statistics. Lei obtained his B.S degree from School of Mathematical Sciences, Nankai University.

石磊，加州大学伯克利分校生物统计学博士生，导师为Jingshen Wang教授和Peng Ding教授。他的研究方向包括因果推断和高维统计学。石磊在南开大学数学科学学院获得学士学位。

内容简介：

The quadratic assignment procedure (QAP) is a popular tool for analyzing network data in medical and social sciences. To test the association between two network measurements represented by two symmetric matrices, QAP calculates the p-value by permuting the units, or equivalently, by simultaneously permuting the rows and columns of one matrix. Its extension to the regression setting, known as the multiple regression QAP, has also gained popularity, especially in psychometrics. However, the statistics theory for QAP has not been fully established in the literature. We fill the gap in this paper. We formulate the network models underlying various QAPs. We derive (a) the asymptotic sampling distributions of some canonical test statistics and (b) the corresponding asymptotic permutation distributions induced by QAP under strong and weak null hypotheses. Task (a) relies on applying the theory of U-statistics, and task (b) relies on applying the theory of double-indexed permutation statistics. The combination of tasks (a) and (b) provides a relatively complete picture of QAP. Overall, our asymptotic theory suggests that using properly studentized statistics in QAP is a robust choice in that it is finite-sample exact under the strong null hypothesis and preserves the asymptotic type one error rate under the weak null hypothesis.

二次分配程序（QAP）是分析医学和社会科学中网络数据的常用工具。为了测试由两个对称矩阵表示的两个网络测量之间的关联，QAP通过排列单位，或等效地，同时排列一个矩阵的行和列来计算p值。其在回归设置中的扩展，称为多元回归QAP，尤其在心理测量学中也获得了广泛应用。然而，QAP的统计理论在文献中尚未完全建立。本文填补了这一空白。主讲人提出支持各种QAP的网络模型。推导了（a）一些经典检验统计量的渐近抽样分布和（b）在强零假设和弱零假设下，由QAP引起的渐近置换分布。任务（a）依赖于U统计量理论的应用，任务（b）依赖于双重索引置换统计量理论的应用。任务（a）和（b）的结合提供了QAP的相对完整的理论框架。总体而言，主讲人的渐近理论表明，在QAP中使用适当的学生化统计量是一种稳健的选择，因为它在强零假设下是有限样本精确的，并且在弱零假设下保持渐近的第一类错误率。