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Low dimensional factor model-based tests for assessing vector correlation in high-dimensional settings

Author

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  • Hyodo, Masashi
  • Nishiyama, Takahiro
  • Narita, Shoichi

Abstract

This study proposes a new test for vector correlation in a high-dimensional framework, while accommodating a low-dimensional latent factor model. Our test, built under low-dimensional factor models, distinguishes from previous normal approximation-based tests, which are valid under a weak-spike structure. We propose a modified RV coefficient for high-dimensional data, and show that its null-limiting distributions follow a weighted mixture of chi-square distributions under a high-dimensional asymptotic regime integrated with weak technical conditions. By applying this asymptotic result and estimation theory of the number of factors in a low-dimensional factor model, we propose a new approximation test for vector correlations. We also derive the asymptotic power function for the proposed test. Lastly, we examine the finite sample and dimensional performance of this test using Monte Carlo simulations.

Suggested Citation

  • Hyodo, Masashi & Nishiyama, Takahiro & Narita, Shoichi, 2026. "Low dimensional factor model-based tests for assessing vector correlation in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:jmvana:v:213:y:2026:i:c:s0047259x25001836
    DOI: 10.1016/j.jmva.2025.105588
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