标题： 具有广义线性结构和发散参数的协方差模型 显示英文标题

标题： Covariance Model with General Linear Structure and Divergent Parameters

摘要： 为了在样本量有限的情况下估计大协方差矩阵，我们通过采用一般链接函数将连续响应向量的协方差与权重矩阵的线性组合连接起来，提出了具有广义线性结构的协方差模型（CMGL）。 在不假设响应分布的情况下，并允许与权重矩阵相关的参数数量发散，我们得到了参数的准最大似然估计量（QMLE），并展示了它们的渐近性质。 此外，提出了一种扩展的贝叶斯信息准则（EBIC）来选择相关的权重矩阵，并证明了EBIC的一致性。 在恒等链接函数下，我们引入了具有闭合形式的普通最小二乘估计量（OLS）。 因此，其计算负担相比QMLE有所减少，并且也研究了OLS的理论性质。 为了评估链接函数的适当性，我们进一步提出了准似然比检验，并获得了其极限分布。 通过模拟研究评估了所提出方法的性能，并通过美国股票市场的分析展示了广义协方差模型的实用性。 显示英文摘要

摘要： For estimating the large covariance matrix with a limited sample size, we propose the covariance model with general linear structure (CMGL) by employing the general link function to connect the covariance of the continuous response vector to a linear combination of weight matrices. Without assuming the distribution of responses, and allowing the number of parameters associated with weight matrices to diverge, we obtain the quasi-maximum likelihood estimators (QMLE) of parameters and show their asymptotic properties. In addition, an extended Bayesian information criteria (EBIC) is proposed to select relevant weight matrices, and the consistency of EBIC is demonstrated. Under the identity link function, we introduce the ordinary least squares estimator (OLS) that has the closed form. Hence, its computational burden is reduced compared to QMLE, and the theoretical properties of OLS are also investigated. To assess the adequacy of the link function, we further propose the quasi-likelihood ratio test and obtain its limiting distribution. Simulation studies are presented to assess the performance of the proposed methods, and the usefulness of generalized covariance models is illustrated by an analysis of the US stock market.