Linear Regression With Gaussian Model Uncertainty: Algorithms and Bounds
Linear Regression With Gaussian Model Uncertainty: Algorithms and Bounds
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DOI：
10.1109/tsp.2007.914323
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发表时间：
2008-06
影响因子：
5.4
通讯作者：
A. Wiesel;Yonina C. Eldar;A. Yeredor
中科院分区：
文献类型：
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作者：
A. Wiesel;Yonina C. Eldar;A. Yeredor
本文考虑混合矩阵中具有随机高斯不确定性的线性回归模型中未知确定性参数向量的估计问题。我们证明了最大似然（ML）估计是一个（去）正则化最小二乘估计，并开发三种替代方法来寻找正则化参数，最大限度地提高了可能性。我们分析的性能使用Cramer-Rao界（CRB）的均方误差，并表明，性能下降，由于不确定性是不严重的，因为可以预期的。接下来，我们再次解决这个问题，假设模型矩阵中的噪声和元素的方差是未知的，并推导出相关的CRB和ML估计。我们比较我们的方法，已知的结果在变量误差（EIV）模型的线性回归。我们讨论了这两种相互竞争的方法之间的相似性，并提供了一个彻底的比较，揭示了他们的理论和实践的差异。
In this paper, we consider the problem of estimating an unknown deterministic parameter vector in a linear regression model with random Gaussian uncertainty in the mixing matrix. We prove that the maximum-likelihood (ML) estimator is a (de)regularized least squares estimator and develop three alternative approaches for finding the regularization parameter that maximizes the likelihood. We analyze the performance using the Cramer-Rao bound (CRB) on the mean squared error, and show that the degradation in performance due the uncertainty is not as severe as may be expected. Next, we address the problem again assuming that the variances of the noise and the elements in the model matrix are unknown and derive the associated CRB and ML estimator. We compare our methods to known results on linear regression in the error in variables (EIV) model. We discuss the similarity between these two competing approaches, and provide a thorough comparison that sheds light on their theoretical and practical differences.