TY - GEN
T1 - The Cramér-Rao bound for estimation-after-selection
AU - Routtenberg, Tirza
AU - Tong, Lang
PY - 2014/1/1
Y1 - 2014/1/1
N2 - In many practical parameter estimation problems, a model selection is made prior to estimation. In this paper, we consider the problem of estimating an unknown parameter of a selected population, where the population is chosen from a population set by using a predetermined selection rule. Since the selection step may have an important impact on subsequent estimation, ignoring it could lead to biased-estimation and an invalid Cramér-Rao bound (CRB). In this work, the mean-square-selected-error (MSSE) criterion is used as a performance measure. The concept of Ψ-unbiasedness is introduced for a given selection rule, Ψ, by using the Lehmann-unbiasedness definition. We derive a non-Bayesian Cramér-Rao-type bound on the MSSE of any Ψ-unbiased estimator. The proposed Ψ-CRB is a function of the conditional Fisher information and is a valid bound on the MSSE. Finally, we examine the Ψ-CRB for different selection rules for mean estimation in a linear Gaussian model.
AB - In many practical parameter estimation problems, a model selection is made prior to estimation. In this paper, we consider the problem of estimating an unknown parameter of a selected population, where the population is chosen from a population set by using a predetermined selection rule. Since the selection step may have an important impact on subsequent estimation, ignoring it could lead to biased-estimation and an invalid Cramér-Rao bound (CRB). In this work, the mean-square-selected-error (MSSE) criterion is used as a performance measure. The concept of Ψ-unbiasedness is introduced for a given selection rule, Ψ, by using the Lehmann-unbiasedness definition. We derive a non-Bayesian Cramér-Rao-type bound on the MSSE of any Ψ-unbiased estimator. The proposed Ψ-CRB is a function of the conditional Fisher information and is a valid bound on the MSSE. Finally, we examine the Ψ-CRB for different selection rules for mean estimation in a linear Gaussian model.
KW - Cramér-Rao bound (CRB)
KW - Non-Bayesian parameter estimation
KW - estimation-after-selection
KW - linear Gaussian model
KW - sample mean selection (SMS) rule
UR - http://www.scopus.com/inward/record.url?scp=84905222335&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2014.6853629
DO - 10.1109/ICASSP.2014.6853629
M3 - Conference contribution
AN - SCOPUS:84905222335
SN - 9781479928927
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 414
EP - 418
BT - 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PB - Institute of Electrical and Electronics Engineers
T2 - 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
Y2 - 4 May 2014 through 9 May 2014
ER -