ON RANK ESTIMATION IN SYMMETRIC MATRICES: THE CASE OF INDEFINITE MATRIX ESTIMATORS
ON RANK ESTIMATION IN SYMMETRIC MATRICES: THE CASE OF INDEFINITE MATRIX ESTIMATORS
复制标题
对称矩阵中的秩估计：不定矩阵估计器的情况
作者：
Stephen G. Donald;Natércia Fortuna;V. Pipiras
在本文中，我们考虑基于未知对称矩阵的对称渐近正态估计来估计该矩阵的秩值。假设相关的正定极限协方差矩阵是一致估计的，并且具有Kronecker积或任意结构。这些假设是标准的，尽管它们排除了矩阵估计器为正或负半正定的情况。我们在这里改写和重新检验了一些已有的等级检验，并引入了一种新的基于矩阵估计的特征值之和的等级检验。我们讨论了对称矩阵的秩估计的两个应用，并提供了一个小型的模拟研究。第一个作者感谢阿尔弗雷德·P·斯隆基金会研究奖学金和美国国家科学基金会赠款SES-0196372的支持。我们感谢联合主编和两位裁判提出了有益的意见和建议。CEMPRE项目--宏观经济研究中心(Centro de EStudos Macroeconómicos e Previsão)--得到葡萄牙科技基金会的支持，该基金会的资金由FEDER和葡萄牙的基金资助。
In this paper we consider estimating the rank of an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix. The related positive definite limit covariance matrix is assumed to be estimated consistently and to have either a Kronecker product or an arbitrary structure. These assumptions are standard although they exclude the case when the matrix estimator is positive or negative semidefinite. We adapt and reexamine here some available rank tests and introduce a new rank test based on the sum of eigenvalues of the matrix estimator. We discuss two applications where rank estimation in symmetric matrices is of interest, and we also provide a small simulation study.The first author acknowledges the support of an Alfred P. Sloan Foundation Research Fellowship and NSF Grant SES-0196372. We thank the co-editor and the two referees for useful comments and suggestions. CEMPRE—Centro de Estudos Macroeconómicos e Previsão—is supported by the Fundação para a Ciência e a Tecnologia, Portugal, through the Programa Operacional Ciência, Tecnologia e Inovação (POCTI) of the Quadro Comunitário de Apoio III, which is financed by FEDER and Portuguese funds.