TY - GEN
T1 - Post-Parameter-Selection Maximum-Likelihood Estimation
AU - Harel, Nadav
AU - Routtenberg, Tirza
N1 - Funding Information:
This work is partially supported by the ISRAEL SCIENCE FOUNDATION (ISF), grant No. 1173/16. The work of N. Harel is partially supported by the Kreitman School of Advanced Graduate Studies.
Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/11
Y1 - 2021/7/11
N2 - Practical multi-parameter estimation problems with limited measurements and unidentifiable scenarios usually involve a preliminary data-based selection stage. Recent works have shown that selection-aware estimation methods outperform state-of-the-art estimators in the sense of post-selection bias and post-selection mean-squared-error (PSMSE). In this paper, we discuss non-Bayesian estimation methods where a subset of parameters is selected for estimation from the full unknown parameter vector by a data-based selection-rule. We present four estimators: the maximum likelihood (ML), the coherent ML, the post-selection ML (PSML), and the coherent PSML. Coherent post-selection estimators force the unselected parameters to zero, and thus, can be implemented in practical high-dimensional problems. Additionally, we develop a low-complexity algorithm, the stochastic approximation PSML (SA-PSML) for practical implementation of the coherent PSML estimator. Simulation results show that the SA-PSML algorithm achieves a lower PSMSE than the coherent ML estimator for sparse vector recovery with the orthogonal matching pursuit (OMP) selection rule.
AB - Practical multi-parameter estimation problems with limited measurements and unidentifiable scenarios usually involve a preliminary data-based selection stage. Recent works have shown that selection-aware estimation methods outperform state-of-the-art estimators in the sense of post-selection bias and post-selection mean-squared-error (PSMSE). In this paper, we discuss non-Bayesian estimation methods where a subset of parameters is selected for estimation from the full unknown parameter vector by a data-based selection-rule. We present four estimators: the maximum likelihood (ML), the coherent ML, the post-selection ML (PSML), and the coherent PSML. Coherent post-selection estimators force the unselected parameters to zero, and thus, can be implemented in practical high-dimensional problems. Additionally, we develop a low-complexity algorithm, the stochastic approximation PSML (SA-PSML) for practical implementation of the coherent PSML estimator. Simulation results show that the SA-PSML algorithm achieves a lower PSMSE than the coherent ML estimator for sparse vector recovery with the orthogonal matching pursuit (OMP) selection rule.
KW - Estimation after parameter selection
KW - orthogonal matching pursuit
KW - post-selection maximum-likelihood
KW - stochastic approximation
KW - unidentifiable models
UR - http://www.scopus.com/inward/record.url?scp=85113462435&partnerID=8YFLogxK
U2 - 10.1109/SSP49050.2021.9513852
DO - 10.1109/SSP49050.2021.9513852
M3 - Conference contribution
AN - SCOPUS:85113462435
T3 - IEEE Workshop on Statistical Signal Processing Proceedings
SP - 446
EP - 450
BT - 2021 IEEE Statistical Signal Processing Workshop, SSP 2021
PB - Institute of Electrical and Electronics Engineers
T2 - 21st IEEE Statistical Signal Processing Workshop, SSP 2021
Y2 - 11 July 2021 through 14 July 2021
ER -