Theory and Methods Papers
Calculating Bivariate Orthonormal Polynomials By Recurrence
Version of Record online: 11 APR 2013
© 2013 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd.
Australian & New Zealand Journal of Statistics
Volume 55, Issue 1, pages 15–24, March 2013
How to Cite
Rayner, J. C. W., Thas, O., Pipelers, P. and Beh, E. J. (2013), Calculating Bivariate Orthonormal Polynomials By Recurrence. Australian & New Zealand Journal of Statistics, 55: 15–24. doi: 10.1111/anzs.12011
- Issue online: 11 APR 2013
- Version of Record online: 11 APR 2013
- categorical data analysis;
- Emerson polynomials;
- orthonormal polynomials;
- smooth tests of goodness of fit
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.