Arbeitspapier
Computationally efficient recursions for top-order invariant polynomials with applications
The top-order zonal polynomials Ck(A),and top-order invariant polynomials Ck1,...,kr(A1,...,Ar)in which each of the partitions of ki,i = 1,..., r,has only one part, occur frequently in multivariate distribution theory, and econometrics - see, for example Phillips (1980, 1984, 1985, 1986), Hillier (1985, 2001), Hillier and Satchell (1986), and Smith (1989, 1993). However, even with the recursive algorithms of Ruben (1962) and Chikuse (1987), numerical evaluation of these invariant polynomials is extremely time consuming. As a result, the value of invariant polynomials has been largely confined to analytic work on distribution theory. In this paper we present new, very much more efficient, algorithms for computing both the top-order zonal and invariant polynomials. These results should make the theoretical results involving these functions much more valuable for direct practical study. We demonstrate the value of our results by providing fast and accurate algorithms for computing the moments of a ratio of quadratic forms in normal random variables.
- Language
-
Englisch
- Bibliographic citation
-
Series: cemmap working paper ; No. CWP07/08
- Classification
-
Wirtschaft
- Subject
-
Ökonometrie
- Event
-
Geistige Schöpfung
- (who)
-
Hillier, Grant
Kan, Raymond
Wang, Xiaolu
- Event
-
Veröffentlichung
- (who)
-
Centre for Microdata Methods and Practice (cemmap)
- (where)
-
London
- (when)
-
2008
- DOI
-
doi:10.1920/wp.cem.2008.0708
- Handle
- Last update
-
10.03.2025, 11:44 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Hillier, Grant
- Kan, Raymond
- Wang, Xiaolu
- Centre for Microdata Methods and Practice (cemmap)
Time of origin
- 2008
Other Objects (12)
COMPUTATIONALLY PRIVATE RANDOMIZING POLYNOMIALS AND THEIR APPLICATIONS
Computing bases for permutation invariant polynomials
Computationally efficient flux variability analysis
Equations for GL Invariant Families of Polynomials
Equations for GL Invariant Families of Polynomials
Quasi–invariant Hermite Polynomials and Lassalle–Nekrasov Correspondence
Computationally efficient design of directionally compliant metamaterials
Two symmetric and computationally efficient Gini correlations
Computationally Efficient Emulators for Earth System Models
A computationally efficient hybrid 2D–3D subwoofer model
A computationally efficient nonparametric approach for changepoint detection
A computationally efficient method for hand–eye calibration
COMPUTATIONALLY PRIVATE RANDOMIZING POLYNOMIALS AND THEIR APPLICATIONS
Computing bases for permutation invariant polynomials
Computationally efficient flux variability analysis
Equations for GL Invariant Families of Polynomials
Equations for GL Invariant Families of Polynomials
Quasi–invariant Hermite Polynomials and Lassalle–Nekrasov Correspondence
Computationally efficient design of directionally compliant metamaterials
Two symmetric and computationally efficient Gini correlations
Computationally Efficient Emulators for Earth System Models
A computationally efficient hybrid 2D–3D subwoofer model
A computationally efficient nonparametric approach for changepoint detection
A computationally efficient method for hand–eye calibration
COMPUTATIONALLY PRIVATE RANDOMIZING POLYNOMIALS AND THEIR APPLICATIONS
Computing bases for permutation invariant polynomials
Computationally efficient flux variability analysis
Equations for GL Invariant Families of Polynomials
Equations for GL Invariant Families of Polynomials
Quasi–invariant Hermite Polynomials and Lassalle–Nekrasov Correspondence
Computationally efficient design of directionally compliant metamaterials
Two symmetric and computationally efficient Gini correlations
Computationally Efficient Emulators for Earth System Models
A computationally efficient hybrid 2D–3D subwoofer model
A computationally efficient nonparametric approach for changepoint detection