This paper explores statistical inference methods for principal component analysis (PCA) in high dimensions, focusing on constructing confidence regions under a spiked covariance model with missing data and heteroskedastic noise. The proposed approach, HeteroPCA, provides distributional guarantees and enables the computation of confidence regions for the principal subspace and entrywise confidence intervals for the covariance matrix. The methodology is fully data-driven and does not require prior knowledge about noise levels.
The study addresses challenges in estimating principal components when dealing with incomplete observations and varying noise levels. It offers insights into developing robust statistical inference procedures that are adaptable to real-world data complexities.
Key points include:
The research enhances previous estimation methods by broadening sample size ranges supported by theory and improving estimation accuracy under challenging conditions.
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by Yuling Yan,Y... at arxiv.org 02-29-2024
https://arxiv.org/pdf/2107.12365.pdfDeeper Inquiries