Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramer-Rao Bound - Foundations and Trends ® in Signal Processing (Paperback)Yonina C. Eldar (author)
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When the parameters to be estimated are deterministic, a popular approach is to bound the MSE achievable within the class of unbiased estimators. Although it is well-known that lower MSE can be obtained by allowing for a bias, in applications it is typically unclear how to choose an appropriate bias.
The book introduces MSE bounds that are lower than the unbiased Cramer-Rao bound (CRB) for all values of the unknowns. It then presents a general framework for constructing biased estimators with smaller MSE than the standard maximum-likelihood (ML) approach, regardless of the true unknown values. Specializing the results to the linear Gaussian model, it derives a class of estimators that dominate least-squares in terms of MSE. It also introduces methods for choosing regularization parameters in penalized ML estimators that outperform standard techniques such as cross validation.
Publisher: now publishers Inc
Number of pages: 160
Weight: 235 g
Dimensions: 234 x 156 x 9 mm