Inference for heteroskedastic PCA with missing data
研究在高维数据中，当存在缺失数据和异方差噪声时，如何构建主成分分析的置信区域，提出基于HeteroPCA估计量的推断方法，并给出非渐近分布保证。
This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly underexplored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in general difficult in high dimension, the challenge is further compounded by the prevalent presence of missing data and heteroskedastic noise. We propose a novel approach to performing valid inference on the principal subspace, on the basis of an estimator called HeteroPCA (Ann. Statist. 50 (2022b) 53–80). We develop nonasymptotic distributional guarantees for HeteroPCA, and demonstrate how these can be invoked to compute both confidence regions for the principal subspace and entrywise confidence intervals for the spiked covariance matrix. Our inference procedures are fully data-driven and adaptive to heteroskedastic random noise, without requiring prior knowledge about the noise levels.