Dimension reduction and coefficient estimation in multivariate linear regression
Dimension reduction and coefficient estimation in multivariate linear regression
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DOI：
10.1111/j.1467-9868.2007.00591.x
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发表时间：
2007-01-01
影响因子：
5.8
通讯作者：
Monteiro, Renato
中科院分区：
文献类型：
--
作者：
Yuan, Ming;Ekici, Ali;Monteiro, Renato
本文介绍了多元线性模型降维和系数估计的一般公式。我们认为，在实践中常用的许多现有的方法可以制定在这个框架中，并有各种限制。我们继续提出一种更灵活和更普遍适用的新方法。所提出的方法可以表示为一种新的惩罚最小二乘估计。我们采用的惩罚是系数矩阵的Ky Fan范数。这样的惩罚鼓励奇异值之间的稀疏性，同时给出收缩系数估计，从而在多元线性模型中同时进行降维和系数估计。我们还提出了一个广义的交叉验证类型的标准的选择的调整参数的惩罚最小二乘。仿真和金融计量经济学的应用表明，新方法的竞争力的性能。非参数因子模型的扩展也进行了讨论。
We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions. We continue to propose a new method that is more flexible and more generally applicable. The method proposed can be formulated as a novel penalized least squares estimate. The penalty that we employ is the coefficient matrix's Ky Fan norm. Such a penalty encourages the sparsity among singular values and at the same time gives shrinkage coefficient estimates and thus conducts dimension reduction and coefficient estimation simultaneously in the multivariate linear model. We also propose a generalized cross-validation type of criterion for the selection of the tuning parameter in the penalized least squares. Simulations and an application in financial econometrics demonstrate competitive performance of the new method. An extension to the non-parametric factor model is also discussed.