INFERENCE FOR HETEROSKEDASTIC PCA WITH MISSING DATA

被引：2

作者：

Yan, Yuling ^{[1
]}

Chen, Yuxin ^{[2
]}

Fan, Jianqing ^{[3
]}

机构：

[1] MIT, Inst Data Syst & Soc, Cambridge, MA 02144 USA

[2] Univ Penn, Wharton Sch, Dept Stat & Data Sci, Philadelphia, PA USA

[3] Princeton Univ, Dept Operat Res & Financial Engn, Princeton, NJ USA

来源：

ANNALS OF STATISTICS | 2024年 / 52卷 / 02期

关键词：

Principal component analysis; confidence regions; missing data; uncertainty quantification; heteroskedastic data; subspace estimation; LOW-RANK MATRIX; CONFIDENCE-INTERVALS; UNCERTAINTY QUANTIFICATION; PRINCIPAL COMPONENTS; SINGULAR SUBSPACES; LARGEST EIGENVALUE; ROBUST REGRESSION; GRADIENT DESCENT; COMPLETION; NOISY;

D O I：

10.1214/24-AOS2366

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 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.

引用

页码：729 / 756

页数：28