Post-Parameter-Selection Maximum-Likelihood Estimation

Nadav Harel, Tirza Routtenberg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publication2021 IEEE Statistical Signal Processing Workshop, SSP 2021
PublisherIEEE Computer Society
Pages446-450
Number of pages5
ISBN (Electronic)9781728157672
DOIs
StatePublished - 11 Jul 2021
Event21st IEEE Statistical Signal Processing Workshop, SSP 2021 - Virtual, Rio de Janeiro, Brazil
Duration: 11 Jul 202114 Jul 2021

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings
Volume2021-July

Conference

Conference21st IEEE Statistical Signal Processing Workshop, SSP 2021
Country/TerritoryBrazil
CityVirtual, Rio de Janeiro
Period11/07/2114/07/21

Keywords

  • Estimation after parameter selection
  • orthogonal matching pursuit
  • post-selection maximum-likelihood
  • stochastic approximation
  • unidentifiable models

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

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