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
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...
Notes
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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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© 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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Latest
Bounds on Estimation- Published:
- 22 January 2015
DOI: https://doi.org/10.1007/978-1-4471-5102-9_69-2
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Bounds on Estimation- Published:
- 11 February 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_69-1