TY - GEN
T1 - A new lower bound on the mean-square error of biased estimators
AU - Todros, Koby
AU - Tabrikian, Joseph
PY - 2008/12/1
Y1 - 2008/12/1
N2 - In this paper, the class of lower bounds on the MSE of unbiased estimators, derived in our previous work, is extended to the case of biased estimation. The proposed class is derived by projecting the estimation error on a Hilbert subspace of 2, which contains linear transformations of elements in the domain of an integral transform of the likelihood-ratio function. It is shown that some well known bounds can be derived from the proposed class by modifying the kernel of the integral transform. By decomposing the projection of the estimation error into bias-independent and bias-dependent components, the proposed class is minimized with respect to the bias function subject to a bounded 2-norm of the bias-dependent component. A new computationally manageable bound is derived from the proposed class using the kernel of the weighted Fourier transform. The bound is applied for exploring the bias-variance tradeoff in the problem of direction-of-arrival estimation.
AB - In this paper, the class of lower bounds on the MSE of unbiased estimators, derived in our previous work, is extended to the case of biased estimation. The proposed class is derived by projecting the estimation error on a Hilbert subspace of 2, which contains linear transformations of elements in the domain of an integral transform of the likelihood-ratio function. It is shown that some well known bounds can be derived from the proposed class by modifying the kernel of the integral transform. By decomposing the projection of the estimation error into bias-independent and bias-dependent components, the proposed class is minimized with respect to the bias function subject to a bounded 2-norm of the bias-dependent component. A new computationally manageable bound is derived from the proposed class using the kernel of the weighted Fourier transform. The bound is applied for exploring the bias-variance tradeoff in the problem of direction-of-arrival estimation.
KW - Bias-variance tradeoff
KW - Biased estimation
KW - Mean-square-error bounds
KW - Parameter estimation
UR - http://www.scopus.com/inward/record.url?scp=62749161455&partnerID=8YFLogxK
U2 - 10.1109/EEEI.2008.4736634
DO - 10.1109/EEEI.2008.4736634
M3 - Conference contribution
AN - SCOPUS:62749161455
SN - 9781424424825
T3 - IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings
SP - 745
EP - 749
BT - 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
T2 - 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2008
Y2 - 3 December 2008 through 5 December 2008
ER -