On Estimation of the Noise Variance in High Dimensional Probabilistic Principal Component Analysis
高维概率主成分分析中的噪声方差估计
Summary 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 for 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 by…