报告题目：Likelihood ratio test on high-dimensional block compound symmetry covariance structure
报 告 人：解俊山 教授
工作单位：河南大学 数学与统计学院
报告时间：2024年9月28日15:00-18:00
报告地点：数信学院305报告室
报告摘要：
In this talk, we will consider the high-dimensional likelihood ratio (LR) test on the block compound symmetric covariance structure of the multivariate Gaussian population. When the dimension of each block divergences as the sample size tends to infinity, we first establish the asymptotic normality and the moderate deviation principle of the logarithmic LR statistic. We also consider the phase transition of Wilk's phenomenon, and establish the necessary and sufficient conditions for Wilk's phenomenon on the asymptotical distribution of the logarithmic LR statistic. Moreover, the asymptotical expansion error of it under more general assumptions is also obtained. Some numerical simulations demonstrate the efficiency of the proposed method in high-dimensional BCS test and verify the accuracy of the theoretical analysis results.
报告人简介：
解俊山，河南大学数学与统计学院教授，博士生导师，美国明尼苏达大学、香港浸会大学访问学者。中国现场统计研究会理事；中国现场统计研究会多元分析应用专业委员会常务理事。主要研究方向为高维统计推断、随机矩阵理论和概率极限理论。主持完成国家自然科学基金、河南省自然科学基金等多项。以第一作者（或通讯作者）在国内外重要概率统计学术期刊发表SCI论文近30篇。
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