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

Weiping Zhang, Baisuo Jin and Zhidong Bai

Biometrika, 2021, vol. 108, issue 4, 933-946

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.

Keywords: Block-structured matrix; Clustering; Eigendecomposition; Random matrix; U-statistic (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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