2013/05/31 by Marten Wegkamp, Yue Zhao · 31 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Copula (linguistics) #Diagonal #Estimator #Financial Risk and Volatility Modeling #Matrix norm #Norm (philosophy) #Operator norm #Random variable #Statistical Methods and Inference #Upper and lower bounds #stat.ML
paper · pdf · doi:10.3150/14-bej690
published in Bernoulli 22(2) (Chapman and Hall London) · Published at http://dx.doi.org/10.3150/14-BEJ690 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
openalex publication_date 2015/11/09 · arxiv created 2016/02/15 · arxiv updated 2016/02/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the adaptive estimation of copula correlation matrix Σ 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 Σ is the plug-in estimator \widehatΣ with Kendall’s tau statistic. We first obtain a sharp bound on the operator norm of \widehatΣ-Σ. Then we study a factor model of Σ, for which we propose a refined estimator \widetildeΣ by fitting a low-rank matrix plus a diagonal matrix to \widehatΣ using least squares with a nuclear norm penalty on the low-rank matrix. The bound on the operator norm of \widehatΣ-Σ serves to scale the penalty term, and we obtain finite sample oracle inequalities for \widetildeΣ. We also consider an elementary factor copula model of Σ, for which we propose closed-form estimators. All of our estimation procedures are entirely data-driven.