Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors


Hillier, Grant, Kan, Raymond and Wang, Xiaolu (2008) Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors. London, GB, Centre for Microdata Methods and Practice (CEMMAP Working Paper, CWP14/08).

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Original Publication URL: http://www.cemmap.ac.uk/wps/cwp1408.pdf

Description/Abstract

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 k-th object of interest, dk say, is expressed in terms of all lower-order dj'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.

Item Type: Monograph (Working Paper)
Related URLs:
Subjects: H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > School of Social Sciences > Economics
University Structure - Pre August 2011 > School of Management
ePrint ID: 55071
Date Deposited: 06 Aug 2008
Last Modified: 27 Mar 2014 18:37
URI: http://eprints.soton.ac.uk/id/eprint/55071

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