香港大学姚建峰教授将于3月10日访问哈工大数学系并做学术报告。欢迎感兴趣的老师和同学参加。

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

时间：2016年3月10日 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.