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Calculating Cumulants of a Taylor Expansion of a Multivariate Function

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  • Kamanzi‐wa‐Binyavanga

Abstract

A method, which we believe is simpler and more transparent than the one due to McCullagh (1984), is described for obtaining the cumulants of a scalar multivariate stochastic Taylor expansion. Its generalisation is also suggested. An important feature, previously not reported, is that the expansion of every cumulant of order≥ 2 is made up of separate subseries. In order to handle certain frequently occurring sums over permutations of members of compound index sets, we introduce a new notation [m]*, where m is a positive integer. Une méthode plus simple et plus transparente que celle de McCullagh (1984), est décrite pour obtenir les cumulants d'une expansion de Taylor scalaire, stochastique à plusieurs variables. Sa généralisation est aussi suggérée. Une caractéristique importante pas signalée auparavant est que l'expansion de chaque cumulant de l'ordre ≥ 2 est composée de sous‐séries séparées. Pour pouvoir traiter certaines sommes qui apparaissent fréquemment sur des permutations des membres des ensembles d'indices composés, nous introduisons une nouvelle notation [m], où m est un entier relatif appositif.

Suggested Citation

  • Kamanzi‐wa‐Binyavanga, 2009. "Calculating Cumulants of a Taylor Expansion of a Multivariate Function," International Statistical Review, International Statistical Institute, vol. 77(2), pages 212-221, August.
    • Handle: RePEc:bla:istatr:v:77:y:2009:i:2:p:212-221
    DOI: 10.1111/j.1751-5823.2008.00058.x
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    1. Marsh, Patrick, 2004. "Transformations For Multivariate Statistics," Econometric Theory, Cambridge University Press, vol. 20(5), pages 963-987, October.
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