From Model Selection to Adaptive Estimation

Lucien Birgé and Pascal Massart
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Lucien Birgé: Université Paris VI and URA CNRS 1321
Pascal Massart: Université Paris Sud and URA CNRS 743

Chapter 4 in Festschrift for Lucien Le Cam, 1997, pp 55-87 from Springer

Abstract: 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.

Date: 1997
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DOI: 10.1007/978-1-4612-1880-7_4

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