## Analysis of the copula correlation matrix for meta-elliptical distributions

author: Yue Zhao, Department of Statistical Science, Cornell University
published: Oct. 6, 2014,   recorded: December 2013,   views: 2068
Categories Download slides: nipsworkshops2013_zhao_matrix_01.pdf (557.4 KB) Streaming Video Help

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We study the copula correlation matrix \$\Sigma\$ for elliptical copulas. In this context, the correlations are connected to Kendall's tau through a sine function transformation. Hence, a natural estimate for \$\Sigma\$ is the plug-in estimator \$\widehat\Sigma\$ with Kendall's tau statistics. In this talk, we first obtain a sharp bound on the operator norm of \$\widehat \Sigma - \Sigma\$. Then, we study a factor model for \$\Sigma\$, for which we propose a refined estimator \$\widetilde\Sigma\$ by fitting a low-rank matrix plus a diagonal matrix to \$\widehat\Sigma\$ using least squares with a nuclear norm penalty on the low-rank matrix. The bound on the operator norm \$\widehat \Sigma - \Sigma\$ serves to scale the penalty term, and we obtain finite sample oracle inequalities for \$\widetilde\Sigma\$. If time permits, we may also present two estimators based on suitably truncated eigen-decompositions of \$\widehat\Sigma\$, one for an elementary factor model and the other for the regime where \$d\$ is proportional to the sample size. (with Marten Wegkamp)

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