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 報(bào)告題目：Estimation and Optimal Structure Selection of High-Dimensional Toeplitz Covariance Structure
    主講人：潘建新教授（英國曼徹斯特大學(xué)）
    時(shí)間：2020年1月2日（周四）15:30 p.m.
    地點(diǎn)：北院卓遠(yuǎn)樓305會(huì)議室
    主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)院

    摘要：The estimation of structured covariance matrix arises in many applications. An appropriate covariance structure improves the accuracy of covariance estimation and increases the efficiency of the mean parameter estimation in statistical models. For example, a good estimation of covariance structures leads to accurate trajectory predictions for longitudinal data and time series data. In this paper we propose a novel statistical method that is able to select the optimal Toeplitz structure and estimate the high-dimensional covariance matrix simultaneously. Entropy loss functions with nonconvex penalties are employed as matrix-discrepancy measures, under which the optimal covariance structure and the selection of the associated Toeplitz structures are made, simultaneously. The resulting Toeplitz structured covariance estimators are guaranteed to be positive definite, unbiased and selection consistent. Asymptotic theories are derived and simulation studies are conducted, showing a very high accurate Toeplitz covariance structure estimation. The proposed method is also applied to real data practices, demonstrating its good performance in covariance estimation in practice.

    主講人簡介：
    潘建新教授，英國曼徹斯特大學(xué)(University of Manchester)數(shù)學(xué)學(xué)院終身教授，英國倫敦圖靈數(shù)據(jù)科學(xué)研究院（The Turing Institute)研究員，英國皇家統(tǒng)計(jì)學(xué)會(huì)(The Royal Statistical Society) 會(huì)士（Fellow）, 國際統(tǒng)計(jì)學(xué)會(huì)（International Statistical Institute）當(dāng)選會(huì)員（elected member）和美國數(shù)理統(tǒng)計(jì)學(xué)會(huì)（Institute of Mathematical Statistics）會(huì)員。統(tǒng)計(jì)學(xué)雜志Biometrics、Biometrical Journal 及Journal of Multivariate Analysis 編委（Associated Editor）。1996年在香港浸會(huì)大學(xué)獲得統(tǒng)計(jì)學(xué)博士學(xué)位，之后到英國洛桑(Rothamsted)實(shí)驗(yàn)中心從事博士后研究。2002年10月加盟曼徹斯特大學(xué)數(shù)學(xué)學(xué)院，先后仼講師(2002)、高級(jí)講師(2004)、Reader(2005)。2006年被曼徹斯特大學(xué)聘為終身教授，并兼任曼徹斯特大學(xué)醫(yī)學(xué)院研究員。曾擔(dān)任曼大數(shù)學(xué)學(xué)院概率統(tǒng)計(jì)系系主任。致力于統(tǒng)計(jì)學(xué)領(lǐng)域內(nèi)復(fù)雜數(shù)據(jù)模型的理論研究及其在醫(yī)學(xué)、金融及工業(yè)上的應(yīng)用，取得了多項(xiàng)創(chuàng)新性研究成果。成果發(fā)表在包括Journal of the American Statistical Association和Biometrika在內(nèi)的統(tǒng)計(jì)學(xué)主流期刊上。已發(fā)表學(xué)術(shù)論文100余篇，出版學(xué)術(shù)專著2部(Growth Curve Models and Statistical Diagnostics 和 Case-Deletion Diagnostics in Linear Mixed Models)，其中1部于2002年由Springer出版社出版。已指導(dǎo)18名博士研究生并獲得學(xué)位。