DocumentCode :
809673
Title :
MSE Bounds With Affine Bias Dominating the CramÉr–Rao Bound
Author :
Eldar, Yonina C.
Author_Institution :
Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa
Volume :
56
Issue :
8
fYear :
2008
Firstpage :
3824
Lastpage :
3836
Abstract :
In continuation to an earlier work, we further develop bounds on the mean-squared error (MSE) when estimating a deterministic parameter vector thetas0 in a given estimation problem, as well as estimators that achieve the optimal performance. The traditional Cramer-Rao (CR) type bounds provide benchmarks on the variance of any estimator of thetas0 under suitable regularity conditions, while requiring a priori specification of a desired bias gradient. To circumvent the need to choose the bias, which is impractical in many applications, it was suggested in our earlier work to directly treat the MSE, which is the sum of the variance and the squared-norm of the bias. While previously we developed MSE bounds assuming a linear bias vector, here we study, in the same spirit, affine bias vectors. We demonstrate through several examples that allowing for an affine transformation can often improve the performance significantly over a linear approach. Using convex optimization tools we show that in many cases we can choose an affine bias that results in an MSE bound that is smaller than the unbiased CR bound for all values of thetas0. Furthermore, we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists, by performing an affine transformation of the standard maximum likelihood (ML) estimator. This leads to estimators that result in a smaller MSE than ML for all possible values of thetas0.
Keywords :
maximum likelihood estimation; mean square error methods; optimisation; vectors; Cramer-Rao bound; MSE; affine bias vectors; affine transformation; convex optimization; deterministic parameter vector estimation; maximum likelihood estimation; mean-squared error bound; Chromium; Density measurement; Estimation error; Helium; Maximum likelihood estimation; Minimax techniques; Parameter estimation; Probability density function; Vectors; Wireless communication; Affine bias; CramÉr–Rao bound (CRB); biased estimation; dominating estimators; maximum likelihood; mean-squared error (MSE) bounds; minimax bounds;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2008.925584
Filename :
4567652
Link To Document :
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