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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:169

Article

Perreault, Samuel¹  Duchesne, Thierry¹  Neslehova, Johanna G.² 

[1] Univ Laval, Dept Math & Stat, Quebec City, PQ, Canada

[2] McGill Univ, Dept Math & Stat, Montreal, PQ, Canada

关键词: Agglomerative clustering;    Constrained maximum likelihood;    Copula;    Kendall's tau;    Parameter clustering;    Shrinkage;   

DOI  :  10.1016/j.jmva.2018.10.009

来源: Elsevier

【 摘 要 】

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 < d. The new estimator can also be much more efficient in finite samples even in the unstructured case K = d, although there is no gain asymptotically. When the distribution of the data is elliptical, the results extend to linear correlation matrices and their inverses. The procedure is illustrated on financial stock returns. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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