報告人：李衛明 教授

報告題目：High-Dimensional Precision Matrix Quadratic Forms: Estimation Framework for p > n

報告時間：2026年4月14日（周二）13：30-14：30

報告地點：云龍校區6號樓304報告廳

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

李衛明，上海財經大學統計與數據科學學院教授，研究領域包括高維統計分析，隨機矩陣理論等。在AOS、JRSS-B、JASA等期刊發表論文30余篇。主持和參與多個國家自然科學基金項目。現任SCI期刊CSDA副主編。

報告摘要：

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.