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Data-driven kernel representations for sampling with an unknown block dependence structure under correlation constraints

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  • Perrin, G.
  • Soize, C.
  • Ouhbi, N.

Abstract

The multidimensional Gaussian kernel-density estimation (G-KDE) is a powerful tool to identify the distribution of random vectors when the maximal information is a set of independent realizations. For these methods, a key issue is the choice of the kernel and the optimization of the bandwidth matrix. To optimize these kernel representations, two adaptations of the classical G-KDE are presented. First, it is proposed to add constraints on the mean and the covariance matrix in the G-KDE formalism. Secondly, it is suggested to separate in different groups the components of the random vector of interest that could reasonably be considered as independent. This block by block decomposition is carried out by looking for the maximum of a cross-validation likelihood quantity that is associated with the block formation. This leads to a tensorized version of the classical G-KDE. Finally, it is shown on a series of examples how these two adaptations can improve the nonparametric representations of the densities of random vectors, especially when the number of available realizations is relatively low compared to their dimensions.

Suggested Citation

  • Perrin, G. & Soize, C. & Ouhbi, N., 2018. "Data-driven kernel representations for sampling with an unknown block dependence structure under correlation constraints," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 139-154.
    • Handle: RePEc:eee:csdana:v:119:y:2018:i:c:p:139-154
    DOI: 10.1016/j.csda.2017.10.005
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    References listed on IDEAS

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    1. Filippone, Maurizio & Sanguinetti, Guido, 2011. "Approximate inference of the bandwidth in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3104-3122, December.
    2. Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.
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    5. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
    6. Duong, Tarn & Hazelton, Martin L., 2005. "Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 417-433, April.
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    Cited by:

    1. Perrin, G., 2020. "Adaptive calibration of a computer code with time-series output," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    2. Guillaume Perrin & Christian Soize, 2020. "Adaptive method for indirect identification of the statistical properties of random fields in a Bayesian framework," Computational Statistics, Springer, vol. 35(1), pages 111-133, March.

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