Newest papers

Principal component error in high-dimensional factor models

Alex Bernstein, Lisa R. Goldberg, Nicholas Gunther, Alec N. Kercheval, Tian Lan, Yian Lin, 姚大义 · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20550 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

在统计因素错误模型中,样本可变量矩阵的主要组成部分(或 eigenvectors)作为主要方向的估计,观察变量的集合的共同运动的真正驱动因素。我们将这些估计中的常见实质性错误写成两种可解释的术语的总和,我们展示了几乎确定的无对称的极限,因为变量数量随着样本大小增加而增加。本场景在财务经济学,基因组学,机器学习和信号处理中很常见。外部空间错误测量了从估计到由人口因素暴露所覆盖的子空间的距离。它可以用数据来表达,为样本大小的变量提供估计的地面。在子空间错误是由该子空间内的旋转错误驱动的。由后者的固定的样

Machine translation (Meta M2M100); the English original follows.

Abstract

In a statistical factor model, principal components (or eigenvectors) of a sample covariance matrix serve as estimates of principal directions, the true drivers of co-movement of a collection of observed variables. We write the often substantial error in these estimates as a sum of two interpretable terms, which we show have almost sure asymptotic limits as the number of variables grows with sample size bounded. This scenario is commonplace in financial economics, genomics, machine learning and signal processing. Out-of-subspace error measures the distance from an estimate to the subspace spanned by population factor exposures. It can be expressed in terms of data, providing an estimable floor for asymptotic error. In-subspace error is driven by a rotation error within that subspace, which arises from the fixed sample size of the latent factor returns and cannot be estimated from data alone. We illustrate our error analysis with a three-factor simulation of the US public equity market, showing the dependence of the magnitude of the error and its components on dimension and sample size. In that simulation, out-of-subspace error dominates. Researchers who rely on principal component analysis to estimate factor models can use our results to quantify errors in model-based predictions and attributions.

Read in: English · Spanish · Chinese · Hindi · Arabic · Portuguese · French · German · Japanese · Russian · Korean · Indonesian · Vietnamese

Topics: Principal component analysis, Factor analysis, Mathematics, Statistics, Covariance matrix, Dimension (graph theory)

Sources: OpenAlex (CC0), arXiv, Crossref. Agent Exchange