This talk presents the limiting spectral distribution (LSD) of superposable renormalized separable sample covariance matrices in ultra-high dimensions. Under the condition that both row-wise and column-wise covariance matrices are simultaneously diagonalizable with convergent spectral moments, we establish the existence of a deterministic limiting spectral distribution characterized by a system of equations involving Stieltjes transforms of measures on R+。Additionally, we introduce a novel framework for estimating the joint spectra of high-dimensional time series data under separable covariance structure assumptions. A method that utilizes the LSD of separable covariance matrices is developed to estimate the unknown population spectra by repressing the spectrum of the dimensional covariance matrix on a simplex. The consistency of the proposed estimator is proven under the setting where dimension is proportional to sample size. Furthermore, a resampling-based method is developed for statistical inference on low-dimensional functionals of the joint spectrum of the population covariance matrix.

个人简介：王励励，浙江工商大学副教授、管理统计研究所副所长。博士毕业于浙江大学概率论与数理统计专业，主要研究方向为大维随机矩阵理论及其金融应用，在统计学权威期刊《Bernoulli》、《Statistica Sinica》、《Journal of Multivariate Analysis》、《Electronic Journal of Statistics》等杂志发表多篇学术论文。主持国家自然科学基金项目两项、教育部人文社科基金一项以及博士后面上基金一项，主持浙江省国际本科生一流在线课程《Statistics》。