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Asymptotically invariant sampling and averaging from stationary-like processes

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  • Kallenberg, Olav

Abstract

Given a process X on or , we may form a random sequence [xi]1,[xi]2,... by sampling from X at some independent points [tau]1,[tau]2,... . If X is stationary up to shifts (which holds for broad classes of Markov and Palm processes) and the distribution of ([tau]n) is asymptotically invariant (as in the case of Poisson or Bernoulli sampling, respectively) then ([xi]n) is asymptotically exchangeable, and the associated empirical distribution converges to the corresponding product random measure.

Suggested Citation

  • Kallenberg, Olav, 1999. "Asymptotically invariant sampling and averaging from stationary-like processes," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 195-204, August.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:2:p:195-204
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    Cited by:

    1. Olav Kallenberg, 1999. "Multivariate Sampling and the Estimation Problem for Exchangeable Arrays," Journal of Theoretical Probability, Springer, vol. 12(3), pages 859-883, July.

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