Selective Cramér-Rao Bound for Estimation after Model Selection

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

3 Scopus citations


In many practical parameter estimation problems, such as direction-of-arrival (DOA) estimation, model selection is done prior to estimation. The data-based model selection step affects the subsequent estimation, which may results in a biased estimation and an invalid Cramér-Rao bound (CRB). Additionaly, estimators after model selection are usually assumed to be coherent with the model selection step, such that the deselected parameters are set to zero. In this paper, we show that for coherent estimators an appropriate estimation performance measure is the mean-squared-selected-error (MSSE) criterion. We introduce the concept of selective unbiasedness by using the Lehmann unbiasedness definition. We derive a non-Bayesian Cramér-Rao-type bound on the MSSE of any coherent and selective unbiased estimator. Finally, we demonstrate that the proposed selective CRB (sCRB) is a valid and informative lower bound on the performance of the post-model selection maximum likelihood estimator for linear regression with the Akaikes Information Criterion (AIC) of model selection.

Original languageEnglish
Title of host publication2018 IEEE Statistical Signal Processing Workshop, SSP 2018
PublisherInstitute of Electrical and Electronics Engineers
Number of pages5
ISBN (Print)9781538615706
StatePublished - 29 Aug 2018
Event20th IEEE Statistical Signal Processing Workshop, SSP 2018 - Freiburg im Breisgau, Germany
Duration: 10 Jun 201813 Jun 2018

Publication series

Name2018 IEEE Statistical Signal Processing Workshop, SSP 2018


Conference20th IEEE Statistical Signal Processing Workshop, SSP 2018
CityFreiburg im Breisgau


  • Non-Bayesian estimation
  • coherence estimation
  • estimation after model selection
  • selective Cramér-Rao bound
  • selective inference

ASJC Scopus subject areas

  • Signal Processing
  • Instrumentation
  • Computer Networks and Communications


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