報 告 人：鄭術蓉 教授

報告題目：Large separable sample covariance matrices: joint CLT for linear spectral statistics and its applications

報告時間：2023年10月14日（周六上午9：30 )

報告地點：江蘇師范大學數學與統計學院學術報告廳（靜遠樓1506室）

主辦單位：數學研究院、數學與統計學院、科學技術研究院

報告人簡介：

     鄭術蓉，東北師范大學教授。主要從事大維隨機矩陣理論及高維統計分析的研究。曾在Annals of Statistics, JASA, Biometrika等統計學重要學術期刊上發表多篇學術論文和主持多項國家自然科學基金項目等。現任Annals of Statistics、Statistica Sinica、Journal of Multivariate Analysis等學術期刊編委。

報告摘要：

     This paper studies a group of correlated separable sample covariance matrices which share a latent random matrix but have distinct spatial-temple covariance structures. The entries of the random matrix can be either independent and identically distributed or elliptically correlated across rows. A joint central limit theorem for linear spectral statistics of such covariance matrices is established in high-dimensional frameworks. By utilizing this general result, we extend two classical likelihood ratio tests to high-dimensional situations, including the significance test in a multivariate linear regression and the test for the equality of several covariance matrices.