IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v69y1997i1p55-70.html
   My bibliography  Save this article

Uniform reconstruction of Gaussian processes

Author

Listed:
  • Müller-Gronbach, Thomas
  • Ritter, Klaus

Abstract

We consider a Gaussian process X with smoothness comparable to the Brownian motion. We analyze reconstructions of X which are based on observations at finitely many points. For each realization of X the error is defined in a weighted supremum norm; the overall error of a reconstruction is defined as the pth moment of this norm. We determine the rate of the minimal errors and provide different reconstruction methods which perform asymptotically optimal. In particular, we show that linear interpolation at the quantiles of a certain density is asymptotically optimal.

Suggested Citation

  • Müller-Gronbach, Thomas & Ritter, Klaus, 1997. "Uniform reconstruction of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 55-70, July.
  • Handle: RePEc:eee:spapps:v:69:y:1997:i:1:p:55-70
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00036-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Su, Yingcai & Cambanis, Stamatis, 1993. "Sampling designs for estimation of a random process," Stochastic Processes and their Applications, Elsevier, vol. 46(1), pages 47-89, May.
    2. Thomas Müller-Gronbach & Rainer Schwabe, 1996. "On optimal allocations for estimating the surface of a random field," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 239-258, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Delphine Blanke & Céline Vial, 2011. "Estimating the order of mean-square derivatives with quadratic variations," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 85-99, February.
    2. Blanke, Delphine & Vial, Céline, 2008. "Assessing the number of mean square derivatives of a Gaussian process," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1852-1869, October.

    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. Thomas Müller-Gronbach & Rainer Schwabe, 1996. "On optimal allocations for estimating the surface of a random field," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 239-258, December.
    2. D. Benelmadani & K. Benhenni & S. Louhichi, 2020. "The reproducing kernel Hilbert space approach in nonparametric regression problems with correlated observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1479-1500, December.
    3. Karim Benhenni & Mustapha Rachdi & Yingcai Su, 2013. "The effect of the regularity of the error process on the performance of kernel regression estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 765-781, August.
    4. Benhenni, Karim & Su, Yingcai, 2016. "Optimal sampling designs for nonparametric estimation of spatial averages of random fields," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 341-351.
    5. Sze Him Leung & Ji Meng Loh & Chun Yip Yau & Zhengyuan Zhu, 2021. "Spatial Sampling Design Using Generalized Neyman–Scott Process," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(1), pages 105-127, March.
    6. Shykula, Mykola & Seleznjev, Oleg, 2006. "Stochastic structure of asymptotic quantization errors," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 453-464, March.

    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:eee:spapps:v:69:y:1997:i:1:p:55-70. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.