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Equidistant and D-optimal designs for parameters of Ornstein-Uhlenbeck process

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  • Kiselák, Jozef
  • Stehlík, Milan

Abstract

In the present paper we provide a thorough study of small sample and asymptotical comparisons of the efficiencies of equidistant designs taking into account both the parameters of trend [theta], as well as the parameters of covariance function r of the Ornstein-Uhlenbeck process. If only trend parameters are of interest, the designs covering more-or-less uniformly the whole design space are rather efficient. However significant difference between infill asymptotics for trend parameter and covariance parameter is observed. We are proving that the n-point equidistant design for parameter [theta] is D-optimal.

Suggested Citation

  • Kiselák, Jozef & Stehlík, Milan, 2008. "Equidistant and D-optimal designs for parameters of Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1388-1396, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1388-1396
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    References listed on IDEAS

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    1. Goos, Peter & Kobilinsky, Andre & O'Brien, Timothy E. & Vandebroek, Martina, 2005. "Model-robust and model-sensitive designs," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 201-216, April.
    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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    1. Baran, S. & Stehlík, M., 2015. "Optimal designs for parameters of shifted Ornstein–Uhlenbeck sheets measured on monotonic sets," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 114-124.
    2. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2014. "‘Nearly’ universally optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1103-1112.
    3. Dette, Holger & Schorning, Kirsten & Konstantinou, Maria, 2017. "Optimal designs for comparing regression models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 273-286.
    4. Baran, Sándor & Sikolya, Kinga & Stehlík, Milan, 2013. "On the optimal designs for the prediction of Ornstein–Uhlenbeck sheets," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1580-1587.
    5. Boukouvalas, A. & Cornford, D. & Stehlík, M., 2014. "Optimal design for correlated processes with input-dependent noise," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1088-1102.

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