光華講壇——社會(huì)名流與企業(yè)家論壇第6567期
主 題：Robust estimation of number of factors in high dimensional factor modeling via Spearman's rank correlation matrix利用Spearman秩相關(guān)矩陣對(duì)高維因子模型中因子數(shù)量進(jìn)行穩(wěn)健估計(jì)
主講人：南方科技大學(xué)統(tǒng)計(jì)與數(shù)據(jù)科學(xué)系 李曾副教授
主持人：統(tǒng)計(jì)學(xué)院 林華珍教授
時(shí)間：9月15日 下午16:00-17:00
舉辦地點(diǎn)：柳林校區(qū)弘遠(yuǎn)樓408會(huì)議室
主辦單位：統(tǒng)計(jì)研究中心和統(tǒng)計(jì)學(xué)院 科研處
主講人簡(jiǎn)介：
Dr Li is currently an associate professor in the Department of Statistics and Data Science, Southern University of Science and Technology. Previously she was a postdoctoral fellow in the Department of Statistics at the Pennsylvania State University. Dr. Li obtained her Ph.D. degree from the Department of Statistics and Actuarial Science at the University of Hong Kong. Dr. Li’s research covers random matrix theory and high dimensional statistics.
李曾，南方科技大學(xué)統(tǒng)計(jì)與數(shù)據(jù)科學(xué)系副教授。2017年獲得香港大學(xué)統(tǒng)計(jì)與精算學(xué)系博士學(xué)位，2017-2019年先后在美國(guó)華盛頓大學(xué)、賓夕法尼亞州立大學(xué)從事博士后研究工作，并于2019年入職南方科技大學(xué)。主要研究領(lǐng)域?yàn)殡S機(jī)矩陣?yán)碚?、高維統(tǒng)計(jì)分析等，研究成果發(fā)表于The Annals of Statistics, Scandinavian Journal of Statistics 等國(guó)際統(tǒng)計(jì)學(xué)期刊。
內(nèi)容簡(jiǎn)介：
Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this paper, we introduce a new estimator based on the spectral properties of Spearman’s rank correlation matrix under the high-dimensional setting, where both dimension and sample size tend to infinity proportionally. Our estimator is applicable for scenarios where either the common factors or idiosyncratic errors follow heavy-tailed distributions. We prove that the proposed estimator is consistent under mild conditions. Numerical experiments also demonstrate the superiority of our estimator compared to existing methods, especially for the heavy-tailed case.
確定高維因素建模中的因素?cái)?shù)量是必要的，但具有挑戰(zhàn)性，特別是當(dāng)數(shù)據(jù)是重尾的時(shí)候。在高維環(huán)境下，維數(shù)和樣本量都成比例趨近于無(wú)窮大，本文基于Spearman秩相關(guān)矩陣的譜特性，引入了一種新的估計(jì)量。主講人的估計(jì)器適用于公共因素或特殊誤差遵循重尾分布的情況。主講人證明了所提出的估計(jì)量在溫和條件下是一致的。數(shù)值實(shí)驗(yàn)也證明了該估計(jì)方法與現(xiàn)有方法相比的優(yōu)越性，特別是在重尾情況下。
