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ESTIMATION OF THE KRONECKER COVARIANCE MODEL BY QUADRATIC FORM
Econometric Theory ( IF 1.0 ) Pub Date : 2020-12-17 , DOI: 10.1017/s026646662000050x
Oliver B. Linton , Haihan Tang

We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension n is large relative to the sample size T). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided ${\log }^3n/T\to 0$ . We obtain the limiting distributions of the Lagrange multiplier and Wald tests under both the null and local alternatives concerning the mean vector $\mu $ . Testing linear restrictions of $\mu $ is also investigated. Finally, our methodology is shown to perform well in finite sample situations both when the Kronecker product model is true and when it is not true.



中文翻译:

通过二次形式估计 KRONECKER 协方差模型

我们提出了协方差矩阵的 Kronecker 乘积模型的新估计器,即二次型估计器。我们表明该估计器在大维情况下具有良好的特性(即,横截面维数n相对于样本大小T较大)。特别是,二次型估计量在提供 ${\log }^3n/T\to 0$ 的相对 Frobenius 范数意义上是一致的。 我们获得了关于均值向量$\mu $ 的零和局部备选方案下的拉格朗日乘数和 Wald 检验的极限分布。 测试$\mu $ 的线性限制也在调查中。最后,我们的方法被证明在 Kronecker 产品模型为真和不为真时在有限样本情况下均表现良好。

更新日期:2020-12-17
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