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Optimal designs for parameter estimation of the Ornstein–Uhlenbeck process

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  • Maroussa Zagoraiou
  • Alessandro Baldi Antognini

Abstract

This paper deals with optimal designs for Gaussian random fields with constant trend and exponential correlation structure, widely known as the Ornstein–Uhlenbeck process. Assuming the maximum likelihood approach, we study the optimal design problem for the estimation of the trend µ and the correlation parameter θ using a criterion based on the Fisher information matrix. For the problem of trend estimation, we give a new proof of the optimality of the equispaced design for any sample size (see Statist. Probab. Lett. 2008; 78:1388–1396). We also show that for the estimation of the correlation parameter, an optimal design does not exist. Furthermore, we show that the optimal strategy for µ conflicts with the one for θ, since the equispaced design is the worst solution for estimating the correlation. Hence, when the inferential purpose concerns both the unknown parameters we propose the geometric progression design, namely a flexible class of procedures that allow the experimenter to choose a suitable compromise regarding the estimation's precision of the two unknown parameters guaranteeing, at the same time, high efficiency for both. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Maroussa Zagoraiou & Alessandro Baldi Antognini, 2009. "Optimal designs for parameter estimation of the Ornstein–Uhlenbeck process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 583-600, September.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:5:p:583-600
    DOI: 10.1002/asmb.749
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    References listed on IDEAS

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    1. J P C Kleijnen & W C M van Beers, 2004. "Application-driven sequential designs for simulation experiments: Kriging metamodelling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 876-883, August.
    2. Hao Zhang & Dale L. Zimmerman, 2005. "Towards reconciling two asymptotic frameworks in spatial statistics," Biometrika, Biometrika Trust, vol. 92(4), pages 921-936, December.
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