TY - GEN
T1 - ASYMPTOTICALLY TIGHT MISSPECIFIED BAYESIAN CRAMÉR-RAO BOUND
AU - Rosenthal, Nadav E.
AU - Tabrikian, Joseph
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024/1/1
Y1 - 2024/1/1
N2 - In many applications of estimation theory, the true data model is not perfectly known, leading to mismatch between the assumed model used for parameter estimation and the actual model. The non-Bayesian misspecified Cramér-Rao bound (MCRB) allows considering the effect of model misspecification on the estimator performance, and it has been extended to the Bayesian framework. Unlike the non-Bayesian MCRB, the corresponding Bayesian bound is asymptotically unattainable. In this paper, we derive an asymptotically tight misspecified Bayesian Cramér-Rao bound. We demonstrate that under some mild and common regularity conditions, this bound is asymptotically achieved by the maximum a-posteriori probability (MAP) estimator. The proposed bound is applied to the problems of variance estimation and direction-of-arrival estimation under model misspecification, illustrating its asymptotic attainability by the MAP estimator.
AB - In many applications of estimation theory, the true data model is not perfectly known, leading to mismatch between the assumed model used for parameter estimation and the actual model. The non-Bayesian misspecified Cramér-Rao bound (MCRB) allows considering the effect of model misspecification on the estimator performance, and it has been extended to the Bayesian framework. Unlike the non-Bayesian MCRB, the corresponding Bayesian bound is asymptotically unattainable. In this paper, we derive an asymptotically tight misspecified Bayesian Cramér-Rao bound. We demonstrate that under some mild and common regularity conditions, this bound is asymptotically achieved by the maximum a-posteriori probability (MAP) estimator. The proposed bound is applied to the problems of variance estimation and direction-of-arrival estimation under model misspecification, illustrating its asymptotic attainability by the MAP estimator.
KW - Bayesian bounds
KW - mean-squared-error
KW - misspecified Cramér-Rao bound (MCRB)
KW - model misspecification
UR - http://www.scopus.com/inward/record.url?scp=85195403121&partnerID=8YFLogxK
U2 - 10.1109/ICASSP48485.2024.10448099
DO - 10.1109/ICASSP48485.2024.10448099
M3 - Conference contribution
AN - SCOPUS:85195403121
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 9916
EP - 9920
BT - 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers
T2 - 49th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024
Y2 - 14 April 2024 through 19 April 2024
ER -