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Encyclopedia of Systems and Control pp 1–8Cite as

Bounds on Estimation

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Abstract

We review several universal lower bounds on statistical estimation, including deterministic bounds on unbiased estimators such as Cramér-Rao bound and Barankin-type bound, as well as Bayesian bounds such as Ziv-Zakai bound. We present explicit forms of these bounds, illustrate their usage for parameter estimation in Gaussian additive noise, and compare their tightness.

Keywords

Statistical estimation, Mean-squared error, Cramér-Rao bound, Barankin-type bound, Ziv-Zakai bound

Footnote 1

Introduction

Statistical estimation involves inferring the values of parameters specifying a statistical model from data. The performance of a particular statistical algorithm is measured by the error between the true parameter values and those estimated by the algorithm. However, explicit forms of estimation error are usually difficult to obtain except for the simplest statistical models. Therefore, performance bounds are derived as a way of quantifying estimation accuracy while maintaining...

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Notes

  1. 1.

    This work was supported in part by NSF Grants CCF-1014908 and CCF-0963742, ONR Grant N000141310050, AFOSR Grant FA9550-11-1-0210.

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Author information

Authors and Affiliations

  1. Preston M. Green Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO, USA

    Dr. Arye Nehorai

  2. Department of Electrical Engineering & Computer Science, Colorado School of Mines, Golden, CO, USA

    Gongguo Tang

Authors
  1. Dr. Arye Nehorai
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  2. Gongguo Tang
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Corresponding author

Correspondence to Arye Nehorai .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2015 Springer-Verlag London

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Nehorai, A., Tang, G. (2015). Bounds on Estimation. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_69-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_69-2

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Bounds on Estimation
    Published:
    22 January 2015

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_69-2

  2. Original

    Bounds on Estimation
    Published:
    11 February 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_69-1

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