Calculating Bivariate Orthonormal Polynomials By Recurrence

Summary 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...

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Bibliographic Details
Published in:Australian & New Zealand journal of statistics 2013-03, Vol.55 (1), p.15-24
Main Authors: Rayner, John C. W., Thas, Olivier, Pipelers, Peter, Beh, Eric J.
Format: Article
Language:English
Subjects:
categorical data analysis
copulas
Emerson polynomials
Mathematical analysis
orthonormal polynomials
Random variables
smooth tests of goodness of fit
Statistics
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Summary:Summary 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.
ISSN:1369-1473
1467-842X
DOI:10.1111/anzs.12011