报告题目：Testing Kronecker Product Covariance Matrices for High-dimensional Matrix-Variate Data

主 讲 人：周望

报告时间：2021年10月21日15:00-16:00

报告地点： 腾讯会议 会议 ID：411 278 359

点击链接入会： https://meeting.tencent.com/dm/kzKvLikE1Fqw

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.

主讲人简介：

周望，新加坡国立大学统计与应用概率系教授。主要从事统计学的理论与应用研究，在高维数据估计、高维数据检验、数据降维、大维数据随机矩阵领域取得了重要的成果。迄今为止，在Annals of Probability，Annals of Applied Probability，Annals of Statistics, Journal of American Statistical Association, Journal of Royal Statistical Society（B）, Biometrika, Bernoulli, Journal of Econometrics，Trans. Amer. Math. Soc. 等国际顶级期刊发表论文近60篇。

邀请人：何勇

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