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Uniform reconstruction of Gaussian processes

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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