Arbeitspapier
Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors
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 [19], Hillier, Kan, and Wang [9]). 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 [9] 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 [9] 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.
- Sprache
-
Englisch
- Erschienen in
-
Series: cemmap working paper ; No. CWP14/08
- Klassifikation
-
Wirtschaft
- Thema
-
Multikriteria-Verfahren
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Hillier, Grant
Kan, Raymond
Wang, Xiaolu
- Ereignis
-
Veröffentlichung
- (wer)
-
Centre for Microdata Methods and Practice (cemmap)
- (wo)
-
London
- (wann)
-
2008
- DOI
-
doi:10.1920/wp.cem.2008.1408
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:42 MEZ
Datenpartner
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Objekttyp
- Arbeitspapier
Beteiligte
- Hillier, Grant
- Kan, Raymond
- Wang, Xiaolu
- Centre for Microdata Methods and Practice (cemmap)
Entstanden
- 2008
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