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Statistics and Computing

, Volume 24, Issue 4, pp 615–632 | Cite as

The algebra of interpolatory cubature formulæ for generic nodes

  • Claudia Fassino
  • Giovanni Pistone
  • Eva Riccomagno
Article
  • 141 Downloads

Abstract

We consider the classical problem of computing the expected value of a real function f of the d-variate random variable X using cubature formulæ. We use in synergy tools from Commutative Algebra for cubature rulæ, from elementary orthogonal polynomial theory and from Probability.

Keywords

Design of experiments Cubature formulæ Algebraic statistics Orthogonal polynomials Evaluation of expectations 

Notes

Acknowledgements

G. Pistone is supported by de Castro Statistics Initiative, Collegio Carlo Alberto, Moncalieri Italy. E. Riccomagno worked on this paper while visiting the Department of Statistics, University of Warwick, and the Faculty of Statistics at TU-Dortmund on a DAAD grant. Financial support is gratefully acknowledged. The authors thank Prof. H.P. Wynn, Prof. G. Monegato (Politecnico di Torino) and Prof. Dr. Hans Michael Möller (Technische Universität—Dortmund) for their useful suggestions.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Claudia Fassino
    • 1
  • Giovanni Pistone
    • 2
  • Eva Riccomagno
    • 1
  1. 1.Dipartimento di MatematicaUniversità di GenovaGenovaItaly
  2. 2.Collegio Carlo AlbertoMoncalieriItaly

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