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Calculating bivariate orthonormal polynomials by recurrence

John CW Rayner, Olivier Thas UGent, Peter Pipelers UGent and Eric J Beh (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:
author
organization
year
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.