Analysis of elliptical copula correlation factor model with Kendall's tau

By Marten H. Wegkamp, Yue Zhao. 2013

44 citations recorded by the source corpus.

We study the adaptive estimation of copula correlation matrix $\Sigma$ for the semi-parametric elliptical copula model. 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 $\hat{\Sigma}$ with Kendall's tau statistic. We first obtain a sharp bound on the operator norm of $\hat{\Sigma}-\Sigma$. Then we study a factor model of $\Sigma$, for which we propose a refined estimator $\widetilde{\Sigma}$ by fitting a low-rank matrix plus a diagonal matrix to $\hat{\Sigma}$ using least squares with a nuclear norm penalty on the low-rank matrix. The bound on the operator norm of $\hat{\Sigma}-\Sigma$ serves to scale the penalty term, and we obtain finite sample oracle inequalities for $\widetilde{\Sigma}$. We also consider an elementary factor copula model of $\Sigma$, for which we propose closed-form estimators. All of our estimation procedures are entirely data-driven.

Subfields: Finance, Statistics and Probability

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Citations in the corpus

Kernel‐based tests for joint independence (2016, background): “, 2016) or also non-parametric and semiparametric copula-based correlations (Liu et al., 2012; Xue and Zou, 2012; Wegkamp and Zhao, 2016; Gaißer et al., 2010).”
Robust Covariance Matrix Estimation via Matrix Depth (2015, background): “In fact, there are many works in the literature on scatter matrix estimation for elliptical distributions, including [34, 42] in classical settings and [48, 21, 22, 47, 18, 24, 23, 36, 49] in high dimensional settings.”
Robust covariance and scatter matrix estimation under Huber’s contamination model (2015, background): “In fact, there are many works in the literature on scatter matrix estimation for elliptical distributions, including [34, 42] in classical settings and [48, 21, 22, 47, 18, 24, 23, 36, 49] in high dimensional settings.”