<p><p>Using generating functions, the top-order zonal polynomials that occur in much distribution theory under normality can be recursively related to other symmetric functions (power-sum and elementary symmetric functions, Ruben, Hillier, Kan, and Wang). Typically, in a recursion of this type the <i>k</i>-th object of interest, <i>d<sub>k</sub></i> say, is expressed in terms of all lower-order <i>d<sub>j</sub></i>'s. In Hillier, Kan, and Wang we pointed out that, in the case of top-order zonal polynomials (and generalizations of them), a shorter (i.e., fixed length) recursion can be deduced. The present paper shows that the argument in generalizes to a large class of objects/generating functions. The results thus obtained are then applied to various problems involving quadratic forms in noncentral normal vectors.</p></p>
Authors
Working Paper details
- DOI
- 10.1920/wp.cem.2008.1408
- Publisher
- IFS
Suggested citation
G, Hillier and R, Kan and X, Wang. (2008). Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors. London: IFS. Available at: https://ifs.org.uk/publications/generating-functions-and-short-recursions-applications-moments-quadratic-forms (accessed: 1 July 2024).
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