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Learning block structures in U-statistic-based matrices
[Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis]

Author

Listed:
  • Weiping Zhang
  • Baisuo Jin
  • Zhidong Bai

Abstract

SummaryWe introduce a conceptually simple, efficient and easily implemented approach for learning the block structure in a large matrix. Using the properties of U-statistics and large-dimensional random matrix theory, the group structure of many variables can be directly identified based on the eigenvalues and eigenvectors of the scaled sample matrix. We also establish the asymptotic properties of the proposed approach under mild conditions. The finite-sample performance of the approach is examined by extensive simulations and data examples.

Suggested Citation

  • Weiping Zhang & Baisuo Jin & Zhidong Bai, 2021. "Learning block structures in U-statistic-based matrices [Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis]," Biometrika, Biometrika Trust, vol. 108(4), pages 933-946.
    • Handle: RePEc:oup:biomet:v:108:y:2021:i:4:p:933-946.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa099
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    Citations

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    Cited by:

    1. Jiayu Lai & Xiaoyi Wang & Kaige Zhao & Shurong Zheng, 2023. "Block-diagonal test for high-dimensional covariance matrices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 447-466, March.
    2. Gong, Tingnan & Zhang, Weiping & Chen, Yu, 2023. "Uncovering block structures in large rectangular matrices," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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