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

In: Models and Algorithms for Global Optimization

Author

Listed:
  • Emily Hamilton

    (Cardiff University)

  • Vippal Savani

    (Cardiff University)

  • Anatoly Zhigljavsky

    (Cardiff University)

Abstract

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.

Suggested Citation

  • Emily Hamilton & Vippal Savani & Anatoly Zhigljavsky, 2007. "Estimating the Minimal Value of a Function in Global Random Search: Comparison of Estimation Procedures," Springer Optimization and Its Applications, in: Aimo Törn & Julius Žilinskas (ed.), Models and Algorithms for Global Optimization, pages 193-214, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-36721-7_13
    DOI: 10.1007/978-0-387-36721-7_13
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    Cited by:

    1. Anatoly Zhigljavsky & Emily Hamilton, 2010. "Stopping rules in k-adaptive global random search algorithms," Journal of Global Optimization, Springer, vol. 48(1), pages 87-97, September.

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