报 告 人： 姚建峰
报告地点： 数学与统计学院104室
报告时间： 2016年03月08日星期二15:00-16:00
主讲人简介：
姚建峰，毕业于巴黎南大学应用数学与统计专业，1990年到1999年担任法国巴黎一大数学与计算机系副教授，2000年至今担任法国雷恩一大数学系教 授，2010年至今同时担任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 和 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。
报告简介： 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.
