Calculating bivariate orthonormal polynomials by recurrence
- Author
- John CW Rayner, Olivier Thas (UGent) , Peter Pipelers (UGent) and Eric J Beh
- Organization
- Abstract
- Emerson gave recurrence formulae for the calculation of orthonormal polynomials for univariate discrete random variables. He claimed that as these were based on the Christoffel-Darboux recurrence relation they were more efficient than those based on the Gram-Schmidt method. This approach was generalised by Rayner and colleagues to arbitrary univariate random variables. The only constraint was that the expectations needed are well-defined. Here the approach is extended to arbitrary bivariate random variables for which the expectations needed are well- defined. The extension to multivariate random variables is clear.
- Keywords
- smooth tests of goodness of fit, Categorical data analysis, copulas, orthonormal polynomials, Emerson polynomials, 2-WAY CONTINGENCY-TABLES, ORTHOGONAL POLYNOMIALS, COPULAS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-2043184
- MLA
- Rayner, John CW, et al. “Calculating Bivariate Orthonormal Polynomials by Recurrence.” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, vol. 55, no. 1, 2013, pp. 15–24, doi:10.1111/anzs.12011.
- APA
- Rayner, J. C., Thas, O., Pipelers, P., & Beh, E. J. (2013). Calculating bivariate orthonormal polynomials by recurrence. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 55(1), 15–24. https://doi.org/10.1111/anzs.12011
- Chicago author-date
- Rayner, John CW, Olivier Thas, Peter Pipelers, and Eric J Beh. 2013. “Calculating Bivariate Orthonormal Polynomials by Recurrence.” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 55 (1): 15–24. https://doi.org/10.1111/anzs.12011.
- Chicago author-date (all authors)
- Rayner, John CW, Olivier Thas, Peter Pipelers, and Eric J Beh. 2013. “Calculating Bivariate Orthonormal Polynomials by Recurrence.” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 55 (1): 15–24. doi:10.1111/anzs.12011.
- Vancouver
- 1.Rayner JC, Thas O, Pipelers P, Beh EJ. Calculating bivariate orthonormal polynomials by recurrence. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS. 2013;55(1):15–24.
- IEEE
- [1]J. C. Rayner, O. Thas, P. Pipelers, and E. J. Beh, “Calculating bivariate orthonormal polynomials by recurrence,” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, vol. 55, no. 1, pp. 15–24, 2013.
@article{2043184,
abstract = {{Emerson gave recurrence formulae for the calculation of orthonormal polynomials for univariate discrete random variables. He claimed that as these were based on the Christoffel-Darboux recurrence relation they were more efficient than those based on the Gram-Schmidt method. This approach was generalised by Rayner and colleagues to arbitrary univariate random variables. The only constraint was that the expectations needed are well-defined. Here the approach is extended to arbitrary bivariate random variables for which the expectations needed are well- defined. The extension to multivariate random variables is clear.}},
author = {{Rayner, John CW and Thas, Olivier and Pipelers, Peter and Beh, Eric J}},
issn = {{1369-1473}},
journal = {{AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS}},
keywords = {{smooth tests of goodness of fit,Categorical data analysis,copulas,orthonormal polynomials,Emerson polynomials,2-WAY CONTINGENCY-TABLES,ORTHOGONAL POLYNOMIALS,COPULAS}},
language = {{eng}},
number = {{1}},
pages = {{15--24}},
title = {{Calculating bivariate orthonormal polynomials by recurrence}},
url = {{http://doi.org/10.1111/anzs.12011}},
volume = {{55}},
year = {{2013}},
}
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