Two-stage estimation after parameter selection

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

3 Scopus citations


In many practical multiparameter estimation problems, no a-priori information exists regarding which parameters are more relevant within a group of candidate unknown parameters. This paper considers the estimation of a selected 'parameter of interest', where the selection is conducted according to a data-based selection rule, Ψ. The selection process introduces a selection bias and creates coupling between decoupled parameters. We propose a two-stage data-acquisition approach that can remove the selection bias and improve estimation performance. We derive a two-stage Cramér-Rao-type bound on the post-selection mean squared error (PSMSE) of any Ψ-unbiased estimator, where the Ψ-unbiasedness is in the Lehmann sense. In addition, we present the two-stage post-selection maximum-likelihood (PSML) estimator. The proposed Ψ-Cramer-Rao bound (CRB), PSML estimator and other existing estimators are examined for a linear Gaussian model, which is widely used in clinical research.

Original languageEnglish
Title of host publication2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016
PublisherIEEE Computer Society
ISBN (Electronic)9781467378024
StatePublished - 24 Aug 2016
Event19th IEEE Statistical Signal Processing Workshop, SSP 2016 - Palma de Mallorca, Spain
Duration: 25 Jun 201629 Jun 2016

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings


Conference19th IEEE Statistical Signal Processing Workshop, SSP 2016
CityPalma de Mallorca


  • Cramér-Rao bound
  • Non-Bayesian estimation after parameter selection
  • post-selection maximum-likelihood (PSML)
  • two-stage model
  • Ψ-unbiasedness

ASJC Scopus subject areas

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


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