报告题目：Power-enhanced Projection Test for High Dimensional Mean Vectors

报告时间：2024年8月12日上午11：00

报告地点：南湖校区老图书馆四楼会议室

主办单位：数学与统计学院

报告人：陈夏

报告人简介：陈夏，陕西师范大学数学与统计学院副院长、教授、博士生导师。武汉大学概率论与数理统计专业博士，北京师范大学统计学博士后。兼任陕西省统计学学会副理事长和中国现场统计研究会多个分会的常务理事或理事。主要从事高维数据统计分析和概率极限理论方面的研究。在国内外统计学重要学术期刊发表论文40余篇，主持国家自然科学基金、教育部人文社科基金和陕西省自然科学基金等国家级和省部级项目多项。在科学出版社出版专著1部、教材1部，获陕西省学位与研究生教育成果奖一等奖、陕西省高等教育优秀教材一等奖和陕西高校科学技术奖二等奖等奖励。

摘要：The projection test has been extensively studied and employed as an effective approach to address the hypothesis testing problem concerning the mean vector in high-dimensional data settings. In this work, we introduce the Power-Enhanced Projection Test (PPT) to mitigate the computational challenges associated with the power loss method in high-dimensional scenarios due to the data-splitting procedure. The PPT incorporates an additional power-enhancement term into the original projection test statistic to compensate for the power loss, obviating the need for multiple estimations of the optimal projection method. Theoretical analysis demonstrates that this power enhancement term converges asymptotically to zero under the null hypothesis, ensuring the control of Type I error. Numerical simulations and real data analysis further validate our conclusions.