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Adaptive estimation of the copula correlation matrix for semiparametic elliptical copulas

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In this joint work with Yue Zhao (Cornell University), we study the adaptive estimation of copula correlation matrix  for elliptical copulas. In this context, the correlations are connected to Kendalls tau through a sine function transformation. Hence, a natural estimate for  is the plug-in estimator b with Kendalls tau statistic. We rst obtain a sharp bound for the operator norm of b 􀀀 . Then, we study a factor model for , for which we propose a re ned estimator e by tting a low-rank matrix plus a diagonal matrix to b using least squares with a nuclear norm penalty on the low-rank matrix. The bound on the operator norm b 􀀀  serves to scale the penalty term, and we obtain nite sample oracle inequalities for e. We also consider an elementary factor model of , for which we propose closed-form estimators. We provide data-driven versions for all our estimation procedures and performance bounds.

This talk is part of the Probability Theory and Statistics in High and Infinite Dimensions series.

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