2020/03/30 by Yue Ju, Ju, Yue, Tianshi Chen +5
Decision Sciences · Engineering · Mathematics · #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Probabilistic and Robust Engineering Design #Statistical and numerical algorithms #Statistics Theory (math.ST) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2003.13435
openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we focus on the influences of the condition number of the regression matrix upon the comparison between two hyper-parameter estimation methods: the empirical Bayes (EB) and the Stein's unbiased estimator with respect to the mean square error (MSE) related to output prediction (SUREy). We firstly show that the greatest power of the condition number of the regression matrix of SUREy cost function convergence rate upper bound is always one larger than that of EB cost function convergence rate upper bound. Meanwhile, EB and SUREy hyper-parameter estimators are both proved to be asymptotically normally distributed under suitable conditions. In addition, one ridge regression case is further investigated to show that when the condition number of the regression matrix goes to infinity, the asymptotic variance of SUREy estimator tends to be larger than that of EB estimator.