報(bào)告人：李衛(wèi)明 教授

報(bào)告題目：High-Dimensional Precision Matrix Quadratic Forms: Estimation Framework for p > n

報(bào)告時(shí)間：2026年4月14日（周二）13：30-14：30

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304報(bào)告廳

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡介：

李衛(wèi)明，上海財(cái)經(jīng)大學(xué)統(tǒng)計(jì)與數(shù)據(jù)科學(xué)學(xué)院教授，研究領(lǐng)域包括高維統(tǒng)計(jì)分析，隨機(jī)矩陣?yán)碚摰取Ｔ?span style="font-family: "times new roman";">AOS、JRSS-B、JASA等期刊發(fā)表論文30余篇。主持和參與多個(gè)國家自然科學(xué)基金項(xiàng)目。現(xiàn)任SCI期刊CSDA副主編。

報(bào)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.