惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

V
Visual Studio Blog
罗磊的独立博客
宝玉的分享
宝玉的分享
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
V
V2EX
酷 壳 – CoolShell
酷 壳 – CoolShell
T
Tailwind CSS Blog
博客园_首页
量子位
月光博客
月光博客
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
博客园 - 司徒正美
人人都是产品经理
人人都是产品经理
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
爱范儿
爱范儿
S
SegmentFault 最新的问题
雷峰网
雷峰网
小众软件
小众软件
博客园 - 聂微东
美团技术团队
Apple Machine Learning Research
Apple Machine Learning Research
WordPress大学
WordPress大学
Jina AI
Jina AI
Hugging Face - Blog
Hugging Face - Blog

stat updates on arXiv.org

A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Revisiting Asymptotic Theory for Principal Component Esti...
[Submitted on 1 Nov 2023 (v1), last revised 13 Aug 2026 (this ve · 2023-11-02 · via stat updates on arXiv.org

View PDF HTML (experimental)

Abstract:It is well known that approximate factor models exhibit rotation indeterminacy. Principal component (PC) estimators are typically analyzed relative to a rotated factor-loading representation, but the commonly used rotation depends on the estimator itself, leaving unclear which fixed population parameters are estimated. We show that any starting representation of the common component can be mapped by a rotation matrix $\bH$, constructed without using the PC estimator or the idiosyncratic errors and unique up to column signs, to a population representation satisfying the same PC normalization as the estimator. Although $\bH$ depends on the starting representation, the resulting representation is invariant to that choice up to simultaneous column sign changes. We call the resulting factors and loadings the pseudo-true (PC-normalized) parameters. Under a general weak factor model allowing signal eigenvalues to diverge at possibly different rates, we establish consistency and asymptotic normality of the PC estimators for these fixed, estimator-independent targets, together with fixed-target asymptotic theory for factor-augmented regressions. The theory thereby justifies confidence intervals for PC-normalized factors, gives loading profiles a fixed-target interpretation, and identifies the population coefficients associated with estimated PC factors in factor-augmented regressions.

Submission history

From: Yoshimasa Uematsu [view email]
[v1] Wed, 1 Nov 2023 16:23:26 UTC (2,406 KB)
[v2] Thu, 13 Aug 2026 23:11:41 UTC (354 KB)