Title

Calculating bivariate orthonormal polynomials by recurrence

RIS ID

77561

Publication Details

Rayner, J. C. W., Thas, O., Pipelers, P. & Beh, E. (2013). Calculating bivariate orthonormal polynomials by recurrence. Australian and New Zealand Journal of Statistics, 55 (1), 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.

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Link to publisher version (DOI)

http://dx.doi.org/10.1111/anzs.12011