曲阜师范大学学报（自然科学版）2024，Vol.50Issue(2)：35-45,11.DOI:10.3969/j.issn.1001-5337.2024.2.035
高斯线性模型正则估计的Cramér-Rao下界
Cramér-Rao lower bound for regular estimation of linear Gaussian models
摘要
Abstract
The Cramér-Rao lower bound of parameter estimation in regularization Gaussian model is studied,and a new CRB is proposed.Under the assumption of unit orthogonality of the design matrix of the linear Gaussian model,the explicit expressions of the variance and CRB of the L1 type regular estimates are given,and numerical calculations are carried out.Furthermore,this article derives the CRB equivalence condition for regular estimation:in a linear Gaussian model,the estimates obtained for CRB are all linear estimators;under the assumption that the regularization term is differentiable,only the regularization term of a quadratic polynomial can make the estimation obtain CRB.Finally,sparse CRB is proposed for esti-mation with sparse features,and its advantages are illustrated both theoretically and practically by compa-ring it with existing CRBs.关键词
Cramér-Rao下界/正则估计/sparse CRBKey words
Cramér-Rao lower bound/regularization estimation/sparse CRB分类
数理科学引用本文复制引用
蔡志鹏,孔令臣..高斯线性模型正则估计的Cramér-Rao下界[J].曲阜师范大学学报（自然科学版）,2024,50(2):35-45,11.基金项目
国家自然科学基金(12371322). （12371322）
