Multivariate Sampling and the Estimation Problem for Exchangeable Arrays

Olav Kallenberg ()
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Olav Kallenberg: Auburn University

Journal of Theoretical Probability, 1999, vol. 12, issue 3, 859-883

Abstract: 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.

Keywords: Stationary processes; exchangeable arrays; functional representations; empirical distributions; limit theorems; consistent estimation (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021692202530

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