Minimax Rank Estimation for Subspace Tracking
Minimax Rank Estimation for Subspace Tracking
复制标题
子空间跟踪的极小极大秩估计
DOI：
10.1109/jstsp.2010.2048070
复制
发表时间：
2009
影响因子：
7.5
通讯作者：
P. Wolfe
中科院分区：
文献类型：
--
作者：
Patrick O. Perry;P. Wolfe
秩估计是一种经典的模型阶数选择问题，出现在各种重要的统计信号和阵列处理系统中，但在现有文献中相对较少得到解决。在这里，我们提出了源于随机矩阵理论的样本协方差渐进，并将它们应用于具有加性高斯白噪声的标准阵列观测模型背景下的最优秩估计问题。这些结果中最重要的结果表明存在相变阈值，低于该阈值，样本协方差的特征值和相关特征向量无法提供有关总体特征值的任何信息。然后，我们开发了一个决策理论排名估计框架，该框架得出基于阈值的简单有序选择规则；然而，与竞争方法相比，它承认渐近极小极大最优性并且无需调整参数。我们分析了排名选择过程的渐近性能，并通过简短的模拟研究得出结论，证明了其在子空间跟踪背景下的实际功效。
Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample covariance asymptotics stemming from random matrix theory, and bring them to bear on the problem of optimal rank estimation in the context of the standard array observation model with additive white Gaussian noise. The most significant of these results demonstrates the existence of a phase transition threshold, below which eigenvalues and associated eigenvectors of the sample covariance fail to provide any information on population eigenvalues. We then develop a decision-theoretic rank estimation framework that leads to a simple ordered selection rule based on thresholding; in contrast to competing approaches, however, it admits asymptotic minimax optimality and is free of tuning parameters. We analyze the asymptotic performance of our rank selection procedure and conclude with a brief simulation study demonstrating its practical efficacy in the context of subspace tracking.