TY - GEN
T1 - A new lower bound on the mean-square error of unbiased estimators
AU - Todros, Koby
AU - Tabrikian, Joseph
PY - 2008/9/16
Y1 - 2008/9/16
N2 - In this paper, a new class of lower bounds on the mean-square-error (MSE) of unbiased estimators of deterministic parameters is proposed. Derivation of the proposed class is performed by approximating each entry of the vector of estimation error in a closed Hilbert subspace of L2. This Hilbert subspace is spanned by a set of linear combinations of elements in the domain of an integral transform of the likelihood-ratio function. It is shown that some well known lower bounds on the MSE of unbiased estimators, can be derived from this class by inferring the integral transform. A new lower bound is derived from this class by choosing the Fourier transform. The bound is computationally manageable and provides better prediction of the signal-to-noise ratio (SNR) threshold region, exhibited by the maximum-likelihood estimator. The proposed bound is compared with other existing bounds in term of threshold SNR prediction in the problem of single tone estimation.
AB - In this paper, a new class of lower bounds on the mean-square-error (MSE) of unbiased estimators of deterministic parameters is proposed. Derivation of the proposed class is performed by approximating each entry of the vector of estimation error in a closed Hilbert subspace of L2. This Hilbert subspace is spanned by a set of linear combinations of elements in the domain of an integral transform of the likelihood-ratio function. It is shown that some well known lower bounds on the MSE of unbiased estimators, can be derived from this class by inferring the integral transform. A new lower bound is derived from this class by choosing the Fourier transform. The bound is computationally manageable and provides better prediction of the signal-to-noise ratio (SNR) threshold region, exhibited by the maximum-likelihood estimator. The proposed bound is compared with other existing bounds in term of threshold SNR prediction in the problem of single tone estimation.
KW - Mean-square-error bounds
KW - Parameter estimation
KW - Threshold SNR
UR - http://www.scopus.com/inward/record.url?scp=51449095834&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2008.4518509
DO - 10.1109/ICASSP.2008.4518509
M3 - Conference contribution
AN - SCOPUS:51449095834
SN - 1424414849
SN - 9781424414840
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3913
EP - 3916
BT - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
T2 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Y2 - 31 March 2008 through 4 April 2008
ER -