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Saturation spaces for regularization methods in inverse problems

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  • Anne Vanhems
  • Jean-Michel Loubes
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    Abstract

    The aim of this article is to characterize the saturation spaces that appear in inverse problems. Such spaces are defined for a regularization method and the rate of convergence of the estimation part of the inverse problem depends on their definition. Here we prove that it is possible to define these spaces as regularity spaces, independent of the choice of the approximation method. Moreover, this intrinsec definition enables us to provide minimax rate of convergence under such assumptions

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    File URL: http://repec.org/esNASM04/up.18098.1075485489.pdf
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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 380.

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    Date of creation: 11 Aug 2004
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    Handle: RePEc:ecm:nasm04:380

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    Keywords: Linear inverse problems; regularization methods; structural econometrics;

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    1. Jean-Michel Loubes, 2002. "Adaptive estimation with soft thresholding penalties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, Netherlands Society for Statistics and Operations Research, vol. 56(4), pages 453-478.
    2. repec:wop:humbsf:2002-50 is not listed on IDEAS
    3. Darolles, Serge & Fan, Yanqin & Florens, Jean-Pierre & Renault, Eric, 2003. "Non Parametric Instrumental Regression," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 228, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2010.
    4. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(06), pages 797-834, December.
    5. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, Econometric Society, vol. 42(6), pages 999-1012, November.
    6. Cohen, Albert & Hoffmann, Marc & Reiß, Markus, 2002. "Adaptive wavelet Galerkin methods for linear inverse problems," SFB 373 Discussion Papers 2002,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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