报告人：李卫明 教授
报告题目：High-Dimensional Precision Matrix Quadratic Forms: Estimation Framework for p > n
报告时间：2026年4月14日（周二）13：30-14：30
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
李卫明，上海财经大学统计与数据科学学院教授，研究领域包括高维统计分析，随机矩阵理论等。在AOS、JRSS-B、JASA等期刊发表论文30余篇。主持和参与多个国家自然科学基金项目。现任SCI期刊CSDA副主编。
报告摘要：
We propose a novel estimation framework for quadratic functionals of precision matrices in high-dimensional settings, particularly in regimes where the feature dimension $p$ exceeds the sample size $n$. Traditional moment-based estimators with bias correction remain consistent when $p<n$ (i.e.,="" $p="" n="" \to="" c="" <1$).="" they="" break="" down="" entirely="" once="">n$, highlighting a fundamental distinction between the two regimes due to rank deficiency and high-dimensional complexity. Our approach resolves these issues by combining a spectral-moment representation with constrained optimization, resulting in consistent estimation under mild moment conditions.
The proposed framework provides a unified approach for inference on a broad class of high-dimensional statistical measures. We illustrate its utility through two representative examples: the optimal Sharpe ratio in portfolio optimization and the multiple correlation coefficient in regression analysis. Simulation studies demonstrate that the proposed estimator effectively overcomes the fundamental $p>n$ barrier where conventional methods fail.