Some statistical applications of Faa di Bruno

Thomas H. Savits

Journal of Multivariate Analysis, 2006, vol. 97, issue 10, 2131-2140

Abstract: The formula of Faa di Bruno is used to calculate higher order derivatives of a composition of functions. In this paper, we first review the multivariate version due to Constantine and Savits [A multivariate Faa di Bruno formula with applications, Trans. AMS 348 (1996) 503-520]. We next derive some useful recursion formulas. These results are then applied to obtain both explicit expressions and recursive formulas for the multivariate Hermite polynomials and moments associated with a multivariate normal distribution. Finally, an explicit expression is derived for the formal Edgeworth series expansion of the distribution of a normalized sum of iid random variables.

Keywords: Faa; di; Bruno; Hermite; polynomials; Edgeworth; expansions (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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