报告人：周望
报告地点：腾讯会议ID:178-598-089
报告时间：2022年09月27日星期二9:30-10:30
报告摘要：
Kronecker product covariance structure provides an efficient way to modeling the inter-correlations of matrix-variate data. In this paper, we propose testing statistics for Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. Central limit theorem is proved for the linear spectral statistics with explicit formulas for mean and covariance functions, which fills in the gap in the literature. We then theoretically justify that the proposed testing statistics have well-controlled sizes and strong powers. To facilitate practical usefulness, we further propose a bootstrap resampling algorithm to approximate the limiting distribution of associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. Extensive numerical studies demonstrate empirically reliable performance of the proposed testing procedure. The approach is then applied to the analysis of a real data set with well-structured portfolio returns. Various estimation approaches lead to contradictory investing strategies in this example, while our testing procedure provides a guideline of selecting the most convincing strategy. This is joint with Yu Long and Xie Jiahui.
主讲人简介：
Zhou Wang，教授，新加坡国立大学，统计和应用概率系，主要从事统计学的理论与应用研究，特别在高维数据估计、高维数据检验、数据降维、大维数据随机矩阵的研究都处于世界的前沿。发表了70多篇高水平文章，其中许多篇发表在统计学领域和概率学领域的顶级杂志，如: Annals of Statistics, Journal of American Statistical Association, Biometrika, Annals of Probability, Probability Theory and Related Fields, Annals of Applied Probability上。一些文章被多位学者引用。Zhou Wang教授主持过多个新加坡国家自然科学基金项目，并应邀在多个国际会议上作大会报告和邀请报告，现为RMTA主编， IMS Fellow.
