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Cumulants and partition lattices IV: a.s. convergence of generalised k-statistics

Part of: Linear inference, regression Parametric inference Stochastic processes

Published online by Cambridge University Press:  09 April 2009

T. P. Speed
T. P. Speed
Affiliation:
C.S.I.R.O., Box 1965, G.P.O., Canberra, A.C.T. 2601, Australia
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Abstract

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Generalised k-statistics associated with multi-indexed arrays of random variables satisfying a generalised form of exchangeability are studied. By showing that they form multi-indexed reversed martingales and that the associated family of σ-fields possesses certain conditional independence properties, conditions for the a.s. convergence of generalised k-statistics are obtained. When the arrays of random variables are sums of independent arrays of independent effects, as is the case with the standard random effects anova models, the limits are identified as the associated generalixed cumulants.

Keywords

cumulantk-statisticpartial exchangeabilityanova modelsvariance component estimationasymptotics

MSC classification

Secondary: 60G42: Martingales with discrete parameter 62F12: Asymptotic properties of estimators 62J10: Analysis of variance and covariance

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 1 , August 1986 , pp. 79 - 94
Copyright
Copyright © Australian Mathematical Society 1986

References

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