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Detection of block-exchangeable structure in large-scale correlation matrices

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  • Perreault, Samuel
  • Duchesne, Thierry
  • Nešlehová, Johanna G.

Abstract

Correlation matrices are omnipresent in multivariate data analysis. When the number d of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case when the variables can be grouped into K clusters with exchangeable dependence; this assumption is often made in applications, e.g., in finance and econometrics. Under this partial exchangeability condition, the corresponding correlation matrix has a block structure and the number of unknown parameters is reduced from d(d−1)∕2 to at most K(K+1)∕2. We propose a robust algorithm based on Kendall’s rank correlation to identify the clusters without assuming the knowledge of K a priori or anything about the margins except continuity. The corresponding block-structured estimator performs considerably better than the sample Kendall rank correlation matrix when K

Suggested Citation

  • Perreault, Samuel & Duchesne, Thierry & Nešlehová, Johanna G., 2019. "Detection of block-exchangeable structure in large-scale correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 400-422.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:400-422
    DOI: 10.1016/j.jmva.2018.10.009
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    2. Chaoubi, Ihsan & Cossette, Hélène & Marceau, Etienne & Robert, Christian Y., 2021. "Hierarchical copulas with Archimedean blocks and asymmetric between-block pairs," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    3. Fuchs, Sebastian & Di Lascio, F. Marta L. & Durante, Fabrizio, 2021. "Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    4. Rutger van der Spek & Alexis Derumigny, 2022. "Fast estimation of Kendall's Tau and conditional Kendall's Tau matrices under structural assumptions," Papers 2204.03285, arXiv.org.
    5. 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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