Two-stage estimation after parameter selection

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3 Scopus citations

Abstract

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
DOIs
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
Volume2016-August

Conference

Conference19th IEEE Statistical Signal Processing Workshop, SSP 2016
Country/TerritorySpain
CityPalma de Mallorca
Period25/06/1629/06/16

Keywords

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

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