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Perturbation of functional tensors with applications to covariance operators

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  • Romain, Yves
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    Abstract

    In this paper, results on the perturbation theory of symmetric operators are given. They concern the tensor extension of a perturbation problem for operators as studied by Fine (Statistics 18 (1987) 401). We consider functional definitions of the tensor product, sum and difference of operators and we study the eigenelement expansions of their perturbations. We show that the main result may be summarized in a simple form called "a perturbation rule for tensor operators". Finally, we indicate briefly how to apply these properties in a multivariate statistical sampling framework.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 58 (2002)
    Issue (Month): 3 (July)
    Pages: 253-264

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    Handle: RePEc:eee:stapro:v:58:y:2002:i:3:p:253-264

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    Keywords: Tensor product Random perturbation theory Covariance operator Eigenvalues perturbation Eigenvectors perturbation Eigenprojectors perturbation;

    References

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    1. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
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    Cited by:
    1. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    2. Boudou, Alain & Romain, Yves, 2002. "On spectral and random measures associated to discrete and continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 145-157, September.

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