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Multivariate Sampling and the Estimation Problem for Exchangeable Arrays

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  • Olav Kallenberg

    (Auburn University)

Abstract

We consider random arrays and the associated empirical distributions obtained by multivariate sampling from a stationary process. Under suitable conditions, one gets convergence toward a separately exchangeable array and its ergodic distribution. The result is related to the statistical problem of estimating the representing function of an exchangeable array. The latter problem is well-posed only for shell-measurable arrays, where the grid processes based on finite sub-arrays form consistent estimates with respect to a suitable norm. In general, the required consistency holds only in the distributional sense for the generated arrays.

Suggested Citation

  • Olav Kallenberg, 1999. "Multivariate Sampling and the Estimation Problem for Exchangeable Arrays," Journal of Theoretical Probability, Springer, vol. 12(3), pages 859-883, July.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:3:d:10.1023_a:1021692202530
    DOI: 10.1023/A:1021692202530
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    References listed on IDEAS

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    1. Kallenberg, Olav, 1989. "On the representation theorem for exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 137-154, July.
    2. 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.
    3. Hoover, D. N., 1989. "Tail fields of partially exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 160-163, October.
    4. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
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