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Estimating the Minimal Value of a Function in Global Random Search: Comparison of Estimation Procedures

  • Emily Hamilton
  • Vippal Savani
  • Anatoly Zhigljavsky
Part of the Optimization and Its Applications book series (SOIA, volume 4)

Summary

In a variety of global random search methods, the minimum of a function is estimated using either one of linear estimators or the the maximum likelihood estimator. The asymptotic mean square errors (MSE) of several linear estimators asymptotically coincide with the asymptotic MSE of the maximum likelihood estimator. In this chapter we consider the non-asymptotic behaviour of different estimators. In particular, we demonstrate that the MSE of the best linear estimator is superior to the MSE of the the maximum likelihood estimator.

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Emily Hamilton
    • 1
  • Vippal Savani
    • 1
  • Anatoly Zhigljavsky
    • 1
  1. 1.School of MathematicsCardiff UniversityUK

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