论文标题
正则化系统识别的渐近理论第一部分：经验贝叶斯高参数估计器
Asymptotic Theory for Regularized System Identification Part I: Empirical Bayes Hyper-parameter Estimator
论文作者
论文摘要
正规化系统识别是过去十年中系统识别的主要进步。尽管已经取得了许多有希望的结果，但它远非完整，还有许多关键问题需要解决。其中之一是渐近理论，该理论是关于模型估计量的收敛性，因为样本量变为无穷大。正则系统识别的现有相关结果是关于各种高参数估计器几乎确定的收敛性。这些结果的一个常见问题是，它们不包含有关影响这些高参数估计量（例如回归矩阵）的收敛性能的因素的信息。在本文中，我们解决了与经验贝叶斯（EB）高参数估计器和过滤的白噪声输入的正则有限脉冲响应模型估计的问题。为了暴露并找到这些因素，我们研究了EB超参数估计量分布的收敛性，以及其相应模型估计器的渐近分布。为了说明，我们运行蒙特卡洛模拟，以显示我们获得的理论结果的功效。
Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them is the asymptotic theory, which is about convergence properties of the model estimators as the sample size goes to infinity. The existing related results for regularized system identification are about the almost sure convergence of various hyper-parameter estimators. A common problem of those results is that they do not contain information on the factors that affect the convergence properties of those hyper-parameter estimators, e.g., the regression matrix. In this paper, we tackle problems of this kind for the regularized finite impulse response model estimation with the empirical Bayes (EB) hyper-parameter estimator and filtered white noise input. In order to expose and find those factors, we study the convergence in distribution of the EB hyper-parameter estimator, and the asymptotic distribution of its corresponding model estimator. For illustration, we run Monte Carlo simulations to show the efficacy of our obtained theoretical results.
