Calculating bivariate orthonormal polynomials by recurrence
(2013) AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS. 55(1). p.15-24- 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.
Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-2043184
- author
- John CW Rayner, Olivier Thas UGent, Peter Pipelers UGent and Eric J Beh
- organization
- year
- 2013
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- copulas, smooth tests of goodness of fit, Categorical data analysis, orthonormal polynomials, Emerson polynomials
- journal title
- AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS
- Aust. N. Z. J. Stat.
- volume
- 55
- issue
- 1
- pages
- 15 - 24
- JCR category
- STATISTICS & PROBABILITY
- JCR impact factor
- 0.42 (2013)
- JCR rank
- 106/119 (2013)
- JCR quartile
- 4 (2013)
- ISSN
- 1369-1473
- DOI
- 10.1111/anzs.12011
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
- I have transferred the copyright for this publication to the publisher
- id
- 2043184
- handle
- http://hdl.handle.net/1854/LU-2043184
- date created
- 2012-02-24 00:25:24
- date last changed
- 2013-04-26 09:25:33
@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},
keyword = {copulas,smooth tests of goodness of fit,Categorical data analysis,orthonormal polynomials,Emerson polynomials},
language = {eng},
number = {1},
pages = {15--24},
title = {Calculating bivariate orthonormal polynomials by recurrence},
url = {http://dx.doi.org/10.1111/anzs.12011},
volume = {55},
year = {2013},
}
- Chicago
- 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.
- 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.
- 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.
- MLA
- Rayner, John CW, Olivier Thas, Peter Pipelers, et al. “Calculating Bivariate Orthonormal Polynomials by Recurrence.” AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 55.1 (2013): 15–24. Print.