Calculating Cumulants of a Taylor Expansion of a Multivariate Function |
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Authors: | Kamanzi-wa-Binyavanga |
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Institution: | Department of Statistics, Walter Sisulu University, South Africa E-mail: |
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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. |
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Keywords: | Affine transformation cumulants Edgeworth expansion stochastic Taylor expansion |
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