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Nonparametric prediction for random fields

Author

Listed:
  • Puri, Madan L.
  • Ruymgaart, Frits H.

Abstract

We study prediction for vector valued random fields in a nonparametric setting. The prediction problem is formulated as the problem if estimating certain conditional expectations and a speed of uniform a.s. convergence is obtained, modifying results for conditional empirical processes derived from series with one-dimensional time. As an alternative to the usual mixing conditions we model the dependence by asymptotic decomposability. This includes linear (which generalizes ARMA) fields and random fields with a finite order Volterra expansion. As an example of a linear field we briefly discuss the finite-differences simulation of the heat equation blurred by additive random noise.

Suggested Citation

  • Puri, Madan L. & Ruymgaart, Frits H., 1993. "Nonparametric prediction for random fields," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 139-156, October.
    • Handle: RePEc:eee:spapps:v:48:y:1993:i:1:p:139-156
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