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学术报告
学术报告
香港大学姚建峰教授学术报告通知
发布人:系统管理员??威尼斯官方网站:2016-03-08?? 浏览次数:367

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题目:On estimation of the noise variance in high-dimensional probabilistic principal component analysis

时间:2016310 上午9:00-10:00

地点:格物楼503

摘要:In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of variables is large in comparison with the sample size. We first unveil the reasons of an observed downward bias of the maximum likelihood estimator of the noise variance when the data dimension is high. We then propose a bias-corrected estimator using random matrix theory and establish its asymptotic normality. The superiority of the new and bias-corrected estimator over existing alternatives is checked by Monte-Carlo experiments with various combinations of (p, n) (dimension and sample size). Next, we construct a new criterion based on the bias-corrected estimator to determine the number of the principal components, and a consistent estimator is obtained. Its good performance is confirmed by simulation study and real data analysis. The bias-corrected estimator is also used to derive new asymptotic for the related goodness-of-fit statistic under the high-dimensional scheme.

简介:姚建峰,现籍法国,原籍常熟杨园,1979年江苏省高考状元,经国家选拔到法国留学,就读于巴黎南大学数学系,先后获得学士、硕士和应用数学博士学位,1999 年在巴黎第一大学获得应用数学 Habilitation à Diriger des Recherches HDR) 文凭 (相当于先前法国国家博士文凭)。先后任教巴黎大学、雷恩大学与香港大学。现担任法国雷恩一大威尼斯官方网站和香港大学统计与精算学系教授。在国际顶尖杂志发表论文近五十篇,其中包括Annals of Statistics, Annals of Applied Probability, Biometrika SIAM Journal on Imaging Science。目前研究方向包括:大维随机矩阵分析,非线性时间序列模型,以及电子图像的处理和数学分析
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