Two-sample tests for principal eigenvalues and eigenvectors in high-dimensional elliptical factor models
Abstract
Changes in principal eigenvalues and eigendirections provide complementary diagnostics of structural instability in factor models, but covariance-based inference can be unreliable under heavy tails. We develop two-sample tests for equality of these features of trace-normalized shape matrices under high-dimensional elliptical factor models. Our approach combines Tyler's identity with orthogonalization and cross-fitting to accommodate general location and precision pilots. We derive a spectral limit theory that yields asymptotically valid calibration without upper-tail moment assumptions on the radial variables, allowing the two populations to have different radial distributions and factor ranks. Simulations demonstrate good size control and gains in size-adjusted power over covariance-based benchmarks under heavy-tailed elliptical distributions. An application to S\&P~500 stock returns illustrates how the tests distinguish changes in relative component strength from changes in component orientation.
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BibTeX
@misc{xu2026twosample,
title = {{Two-sample tests for principal eigenvalues and eigenvectors in high-dimensional elliptical factor models}},
author = {Xinyue Xu and Mengtao Wen and Long Feng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37906},
eprint = {2609.37906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37906},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two-sample tests for principal eigenvalues and eigenvectors in high-dimensional elliptical factor models
AU - Xinyue Xu
AU - Mengtao Wen
AU - Long Feng
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37906
UR - https://arxiv.org/abs/2609.37906
AB - Changes in principal eigenvalues and eigendirections provide complementary diagnostics of structural instability in factor models, but covariance-based inference can be unreliable under heavy tails. We develop two-sample tests for equality of these features of trace-normalized shape matrices under high-dimensional elliptical factor models. Our approach combines Tyler's identity with orthogonalization and cross-fitting to accommodate general location and precision pilots. We derive a spectral limit theory that yields asymptotically valid calibration without upper-tail moment assumptions on the radial variables, allowing the two populations to have different radial distributions and factor ranks. Simulations demonstrate good size control and gains in size-adjusted power over covariance-based benchmarks under heavy-tailed elliptical distributions. An application to S\&P~500 stock returns illustrates how the tests distinguish changes in relative component strength from changes in component orientation.
ER -