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From Model Selection to Adaptive Estimation

In: Festschrift for Lucien Le Cam

Author

Listed:
  • Lucien Birgé

    (Université Paris VI and URA CNRS 1321)

  • Pascal Massart

    (Université Paris Sud and URA CNRS 743)

Abstract

Many different model selection information criteria can be found in the literature in various contexts including regression and density estimation. There is a huge amount of literature concerning this subject and we shall, in this paper, content ourselves to cite only a few typical references in order to illustrate our presentation. Let us just mention AIC, C p , or C L , BIC and MDL criteria proposed by Akaike (1973), Mallows (1973), Schwarz (1978), and Rissanen (1978) respectively. These methods propose to select among a given collection of parametric models that model which minimizes an empirical loss (typically squared error or minus log-likelihood) plus some penalty term which is proportional to the dimension of the model. From one criterion to another the penalty functions differ by factors of log n, where n represents the number of observations.

Suggested Citation

  • Lucien Birgé & Pascal Massart, 1997. "From Model Selection to Adaptive Estimation," Springer Books, in: David Pollard & Erik Torgersen & Grace L. Yang (ed.), Festschrift for Lucien Le Cam, chapter 4, pages 55-87, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1880-7_4
    DOI: 10.1007/978-1-4612-1880-7_4
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    Cited by:

    1. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.

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