IDEAS home Printed from https://ideas.repec.org/p/tiu/tiucen/00a66547-3e9a-4ccf-8c7b-8d62bd7b460e.html
   My bibliography  Save this paper

The Correct Kriging Variance Estimated by Bootstrapping

Author

Listed:
  • den Hertog, D.

    (Tilburg University, Center For Economic Research)

  • Kleijnen, J.P.C.

    (Tilburg University, Center For Economic Research)

  • Siem, A.Y.D.

    (Tilburg University, Center For Economic Research)

Abstract

The classic Kriging variance formula is widely used in geostatistics and in the design and analysis of computer experiments. This paper proves that this formula is wrong. Furthermore, it shows that the formula underestimates the Kriging variance in expectation. The paper develops parametric bootstrapping to estimate the Kriging variance. The new method is tested on several artificial examples and a real-life case study. These results demonstrate that the classic formula underestimates the true Kriging variance.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • den Hertog, D. & Kleijnen, J.P.C. & Siem, A.Y.D., 2004. "The Correct Kriging Variance Estimated by Bootstrapping," Discussion Paper 2004-46, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:00a66547-3e9a-4ccf-8c7b-8d62bd7b460e
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/601354/46.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Sara Sjöstedt‐de Luna & Alastair Young, 2003. "The Bootstrap and Kriging Prediction Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 175-192, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    2. Jack P. C. Kleijnen & Susan M. Sanchez & Thomas W. Lucas & Thomas M. Cioppa, 2005. "State-of-the-Art Review: A User’s Guide to the Brave New World of Designing Simulation Experiments," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 263-289, August.
    3. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
    4. 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.
    5. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    6. Hartman, Linda & Hossjer, Ola, 2008. "Fast kriging of large data sets with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2331-2349, January.
    7. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Other publications TiSEM d8c37ad3-f9a5-4824-986d-2, Tilburg University, School of Economics and Management.
    8. Federica Giummolè & Paolo Vidoni, 2010. "Improved prediction limits for a general class of Gaussian models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 483-493, November.
    9. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    10. Kleijnen, J.P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2008. "Constrained Optimization in Simulation : A Novel Approach," Discussion Paper 2008-95, Tilburg University, Center for Economic Research.
    11. Stinstra, Erwin & den Hertog, Dick, 2008. "Robust optimization using computer experiments," European Journal of Operational Research, Elsevier, vol. 191(3), pages 816-837, December.
    12. Jize Zhang & Alexandros A. Taflanidis & Norberto C. Nadal-Caraballo & Jeffrey A. Melby & Fatimata Diop, 2018. "Advances in surrogate modeling for storm surge prediction: storm selection and addressing characteristics related to climate change," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(3), pages 1225-1253, December.
    13. De Oliveira, Victor & Kone, Bazoumana, 2015. "Prediction intervals for integrals of Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 37-51.
    14. Stinstra, E., 2006. "The meta-model approach for simulation-based design optimization," Other publications TiSEM 713f828a-4716-4a19-af00-e, Tilburg University, School of Economics and Management.
    15. Kleijnen, J.P.C., 2007. "Screening Experiments for Simulation : A Review," Discussion Paper 2007-21, Tilburg University, Center for Economic Research.
    16. Xiao, Ning-Cong & Zuo, Ming J. & Zhou, Chengning, 2018. "A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 330-338.
    17. Gaofeng Jia & Alexandros Taflanidis & Norberto Nadal-Caraballo & Jeffrey Melby & Andrew Kennedy & Jane Smith, 2016. "Surrogate modeling for peak or time-dependent storm surge prediction over an extended coastal region using an existing database of synthetic storms," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 909-938, March.
    18. Paige, John & Fuglstad, Geir-Arne & Riebler, Andrea & Wakefield, Jon, 2022. "Bayesian multiresolution modeling of georeferenced data: An extension of ‘LatticeKrig’," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    19. Mlakar, Miha & Petelin, Dejan & Tušar, Tea & Filipič, Bogdan, 2015. "GP-DEMO: Differential Evolution for Multiobjective Optimization based on Gaussian Process models," European Journal of Operational Research, Elsevier, vol. 243(2), pages 347-361.
    20. Scott L. Rosen & Christopher P. Saunders & Samar K Guharay, 2015. "A Structured Approach for Rapidly Mapping Multilevel System Measures via Simulation Metamodeling," Systems Engineering, John Wiley & Sons, vol. 18(1), pages 87-101, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiucen:00a66547-3e9a-4ccf-8c7b-8d62bd7b460e. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard Broekman (email available below). General contact details of provider: http://center.uvt.nl .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.