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Some statistical applications of Faa di Bruno

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  • Savits, Thomas H.

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.

Suggested Citation

  • Savits, Thomas H., 2006. "Some statistical applications of Faa di Bruno," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2131-2140, November.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2131-2140
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    Cited by:

    1. Lorenzo Garlappi & Georgios Skoulakis, 2009. "Numerical Solutions to Dynamic Portfolio Problems: The Case for Value Function Iteration using Taylor Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 33(2), pages 193-207, March.

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