Estimating high-dimensional dependence structures in models of multivariate datasets is an ongoing challenge. Copulas provide a powerful and intuitive way to model dependence structure in the joint distribution of disparate types of variables. Here, we propose an estimation method for Gaussian copula parameters based on the maximum likelihood estimate of a covariance matrix that includes shrinkage and where all of the diagonal elements are restricted to be equal to 1. We show that this estimation problem can be solved using a numerical solution that optimizes the problem in a block coordinate descent fashion. We illustrate the advantage of our proposed scheme in providing an efficient estimate of sparse Gaussian copula covariance parameters using a simulation study. The sparse estimate was obtained by regularizing the constrained problem using either the least absolute shrinkage and selection operator (LASSO) or the adaptive LASSO penalty, applied to either the covariance matrix or the inverse covariance (precision) matrix. Simulation results indicate that our method outperforms conventional estimates of sparse Gaussian copula covariance parameters. We demonstrate the proposed method for modelling dependence structures through an analysis of multivariate groundfish abundance data obtained from annual bottom trawl surveys in the northeast Pacific from 2014 to 2018. Supplementary materials accompanying this paper appear on-line.

估计多元数据集模型中的高维依赖结构是一个持续的挑战。Copulas 提供了一种强大而直观的方法来对不同类型变量的联合分布中的依赖结构进行建模。在这里，我们提出了一种基于协方差矩阵的最大似然估计的高斯 copula 参数估计方法，该矩阵包括收缩并且所有对角线元素都被限制为等于 1。我们表明可以使用以块坐标下降方式优化问题的数值解。我们说明了我们提出的方案在使用模拟研究提供稀疏高斯 copula 协方差参数的有效估计方面的优势。稀疏估计是通过使用最小绝对收缩和选择算子 (LASSO) 或自适应 LASSO 惩罚（应用于协方差矩阵或逆协方差（精度）矩阵）对约束问题进行正则化而获得的。仿真结果表明，我们的方法优于稀疏高斯 copula 协方差参数的常规估计。我们通过分析从 2014 年到 2018 年东北太平洋年度底拖网调查获得的多元底层鱼类丰度数据，展示了用于建模依赖结构的建议方法。本文随附的补充材料在线出现。仿真结果表明，我们的方法优于稀疏高斯 copula 协方差参数的常规估计。我们通过分析从 2014 年到 2018 年东北太平洋年度底拖网调查获得的多元底层鱼类丰度数据，展示了用于建模依赖结构的建议方法。本文随附的补充材料在线出现。仿真结果表明，我们的方法优于稀疏高斯 copula 协方差参数的常规估计。我们通过分析从 2014 年到 2018 年东北太平洋年度底拖网调查获得的多元底层鱼类丰度数据，展示了用于建模依赖结构的建议方法。本文随附的补充材料在线出现。