Maximum likelihood parameter and rank estimation in reduced-rank multivariate linear regressions
Maximum likelihood parameter and rank estimation in reduced-rank multivariate linear regressions
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DOI：
10.1109/78.553480
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发表时间：
1996-12-01
影响因子：
5.4
通讯作者：
Viberg, M
中科院分区：
文献类型：
--
作者：
Stoica, P;Viberg, M
本文考虑具有任意协方差噪声的降秩线性回归方程的极大似然估计问题，将回归系数的降秩阵参数化为两个满秩因子阵的乘积。这种参数化本质上是无约束的，但它不是唯一的，这使得相关的ML估计问题相当不标准。然而，这个问题是容易处理的，并且得到了如下结果：根据数据协方差及其特征元，给出了回归矩阵的ML估计的显式表达式。此外，对最大似然参数估计的统计性质进行了详细的分析。此外，还提出了一种广义似然比检验(GLRT)来估计回归矩阵的阶。文中还给出了一些模拟实验的结果，为理论结论提供了经验支持。
This paper considers the problem of maximum likelihood (ML) estimation for reduced-rank linear regression equations with noise of arbitrary covariance, The rank-reduced matrix of regression coefficients is parameterized as the product of two full-rank factor matrices. This parameterization is essentially constraint free, but it is not unique, which renders the associated ML estimation problem rather nonstandard. Nevertheless, the problem turns out to be tractable, and the following results are obtained: An explicit expression is derived for the ML estimate of the regression matrix in terms of the data covariances and their eigenelements. Furthermore, a detailed analysis of the statistical properties of the ML parameter estimate is performed. Additionally, a generalized likelihood ratio test (GLRT) is proposed for estimating the rank of the regression matrix. The paper also presents the results of some simulation exercises, which lend empirical support to the theoretical findings.