Cramér-Rao lower bound for regular estimation of linear Gaussian models
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.
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