On convergence of covariance matrix of empirical Bayes hyper-parameter estimator
Yue Ju1
Biqiang Mu2
Tianshi Chen3
1.School of Data Science and Shenzhen Research Institute of Big Data,The Chinese University of Hong Kong,Shenzhen,Shenzhen 518172,Guangdong,China;Division of Decision and Control Systems,School of Electrical Engineering and Computer Science,KTH Royal Institute of Technology,10044 Stockholm,Sweden2.Key Laboratory of Systems and Control,Institute of Systems Science,Academy of Mathematics and System Science,Chinese Academy of Sciences,Beijing 100190,China3.School of Data Science and Shenzhen Research Institute of Big Data,The Chinese University of Hong Kong,Shenzhen,Shenzhen 518172,Guangdong,China
摘要：Regularized system identification has become the research frontier of system identification in the past decade.One related core subject is to study the convergence properties of various hyper-parameter estimators as the sample size goes to infinity.In this paper,we consider one commonly used hyper-parameter estimator,the empirical Bayes(EB).Its convergence in distribution has been studied,and the explicit expression of the covariance matrix of its limiting distribution has been given.However,what we are truly interested in are factors contained in the covariance matrix of the EB hyper-parameter estimator,and then,the convergence of its covariance matrix to that of its limiting distribution is required.In general,the convergence in distribution of a sequence of random variables does not necessarily guarantee the convergence of its covariance matrix.Thus,the derivation of such convergence is a necessary complement to our theoretical analysis about factors that influence the convergence properties of the EB hyper-parameter estimator.In this paper,we consider the regularized finite impulse response(FIR)model estimation with deterministic inputs,and show that the covariance matrix of the EB hyper-parameter estimator converges to that of its limiting distribution.Moreover,we run numerical simulations to demonstrate the efficacy of our theoretical results.
机标关键词：convergencematrixbayescovarianceempiricalestimatorhyper-parameter
论文发表日期：2024-05-05
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：14( 149-162 )
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