Two-stage estimation after parameter selection

Tirza Routtenberg

doi:10.1109/SSP.2016.7551842

Two-stage estimation after parameter selection

Tirza Routtenberg

Department of Electrical & Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 language	English
Title of host publication	2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016
Publisher	Institute of Electrical and Electronics Engineers
ISBN (Electronic)	9781467378024
DOIs	https://doi.org/10.1109/SSP.2016.7551842
State	Published - 24 Aug 2016
Event	19th IEEE Statistical Signal Processing Workshop, SSP 2016 - Palma de Mallorca, Spain Duration: 25 Jun 2016 → 29 Jun 2016

Publication series

Name	IEEE Workshop on Statistical Signal Processing Proceedings
Volume	2016-August

Conference

Conference	19th IEEE Statistical Signal Processing Workshop, SSP 2016
Country/Territory	Spain
City	Palma de Mallorca
Period	25/06/16 → 29/06/16

Keywords

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

Access to Document

10.1109/SSP.2016.7551842

Cite this

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title = "Two-stage estimation after parameter selection",

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 Cram{\'e}r-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.",

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author = "Tirza Routtenberg",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 19th IEEE Statistical Signal Processing Workshop, SSP 2016 ; Conference date: 25-06-2016 Through 29-06-2016",

year = "2016",

month = aug,

day = "24",

doi = "10.1109/SSP.2016.7551842",

language = "English",

series = "IEEE Workshop on Statistical Signal Processing Proceedings",

publisher = "Institute of Electrical and Electronics Engineers",

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Routtenberg, T 2016, Two-stage estimation after parameter selection. in 2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016., 7551842, IEEE Workshop on Statistical Signal Processing Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers, 19th IEEE Statistical Signal Processing Workshop, SSP 2016, Palma de Mallorca, Spain, 25/06/16. https://doi.org/10.1109/SSP.2016.7551842

Two-stage estimation after parameter selection. / Routtenberg, Tirza.
2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016. Institute of Electrical and Electronics Engineers, 2016. 7551842 (IEEE Workshop on Statistical Signal Processing Proceedings; Vol. 2016-August).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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.

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Two-stage estimation after parameter selection

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Conference

Keywords

ASJC Scopus subject areas

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