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Linking the Hoeffding–Sobol and Möbius formulas through a decomposition of Kuo, Sloan, Wasilkowski, and Woźniakowski

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  • Mercadier, Cécile
  • Roustant, Olivier
  • Genest, Christian

Abstract

Extensions of a result of Kuo et al. (2010) are presented which unify the derivation of the Hoeffding–Soboland Möbius decompositions of a multivariate function as a sum of terms of increasing complexity.

Suggested Citation

  • Mercadier, Cécile & Roustant, Olivier & Genest, Christian, 2022. "Linking the Hoeffding–Sobol and Möbius formulas through a decomposition of Kuo, Sloan, Wasilkowski, and Woźniakowski," Statistics & Probability Letters, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:stapro:v:185:y:2022:i:c:s0167715222000335
    DOI: 10.1016/j.spl.2022.109419
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    References listed on IDEAS

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    1. Deheuvels, Paul, 1981. "An asymptotic decomposition for multivariate distribution-free tests of independence," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 102-113, March.
    2. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    3. Ökten, Giray & Liu, Yaning, 2021. "Randomized quasi-Monte Carlo methods in global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    4. C Genest & J G Nešlehová & B Rémillard & O A Murphy, 2019. "Testing for independence in arbitrary distributions," Biometrika, Biometrika Trust, vol. 106(1), pages 47-68.
    5. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
    6. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.
    7. Kojadinovic, Ivan & Holmes, Mark, 2009. "Tests of independence among continuous random vectors based on Cramr-von Mises functionals of the empirical copula process," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1137-1154, July.
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