TY - JOUR
T1 - Uniformly best biased estimators in non-bayesian parameter estimation
AU - Todros, Koby
AU - Tabrikian, Joseph
N1 - Funding Information: Manuscript received November 01, 2010; revised April 29, 2011; accepted May 25, 2011. Date of current version November 11, 2011. This work was supported in part by the Israel Science Foundation (grant No. 1311/08). The authors are with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Communicated by D. Guo, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2011.2159958
PY - 2011/11/1
Y1 - 2011/11/1
N2 - In this paper, a new structured approach for obtaining uniformly best non-Bayesian biased estimators, which attain minimum-mean-square-error performance at any point in the parameter space, is established. We show that if a uniformly best biased (UBB) estimator exists, then it is unique, and it can be directly obtained from any locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived. It is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and its closed-form expression is obtained. The proposed approach is exemplified in two nonlinear estimation problems, where uniformly minimum-variance-unbiased estimators do not exist. In the considered examples, we show that the UBB estimators outperform the corresponding maximum-likelihood estimators in the MSE sense.
AB - In this paper, a new structured approach for obtaining uniformly best non-Bayesian biased estimators, which attain minimum-mean-square-error performance at any point in the parameter space, is established. We show that if a uniformly best biased (UBB) estimator exists, then it is unique, and it can be directly obtained from any locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived. It is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and its closed-form expression is obtained. The proposed approach is exemplified in two nonlinear estimation problems, where uniformly minimum-variance-unbiased estimators do not exist. In the considered examples, we show that the UBB estimators outperform the corresponding maximum-likelihood estimators in the MSE sense.
KW - Locally best biased (LBB) estimators
KW - minimum-mean-square-error (MMSE)
KW - non-Bayesian theory
KW - parameter estimation
KW - uniformly best biased (UBB) estimators
UR - http://www.scopus.com/inward/record.url?scp=81255212002&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/TIT.2011.2159958
DO - https://doi.org/10.1109/TIT.2011.2159958
M3 - Article
SN - 0018-9448
VL - 57
SP - 7635
EP - 7647
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 11
M1 - 5893945
ER -