Slope heuristics: overview and implementation. Model selection is a general paradigm which includes many statistical problems. One of the most fruitful and popular approaches to carry it out is the minimization of a penalized criterion. L. Birgé and P. Massart [Probab. Theory Relat. Fields 138, No. 1–2, 33–73 (2007; Zbl 1112.62082)] have proposed a promising data-driven method to calibrate such criteria whose penalties are known up to a multiplicative factor: the “slope heuristics”. Theoretical works validate this heuristic method in some situations and several papers report a promising practical behavior in various frameworks. The purpose of this work is twofold. First, an introduction to the slope heuristics and an overview of the theoretical and practical results about it are presented. Second, we focus on the practical difficulties occurring for applying the slope heuristics. A new practical approach is carried out and compared to the standard dimension jump method. All the practical solutions discussed in this paper in different frameworks are implemented and brought together in a Matlab graphical user interface called CAPUSHE. Supplemental Materials containing further information and an additional application, the CAPUSHE package and the datasets presented in this paper, are available on the journal Web site.

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  1. Brunel, Élodie; Mas, André; Roche, Angelina: Non-asymptotic adaptive prediction in functional linear models (2016)
  2. Comte, Fabienne; Rebafka, Tabea: Nonparametric weighted estimators for biased data (2016)
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  4. Baudry, Jean-Patrick: Estimation and model selection for model-based clustering with the conditional classification likelihood (2015)
  5. Baudry, Jean-Patrick; Celeux, Gilles: EM for mixtures (2015)
  6. Comte, Fabienne; Genon-Catalot, Valentine: Adaptive Laguerre density estimation for mixed Poisson models (2015)
  7. Kappus, Johanna; Mabon, Gwennaëlle: Adaptive density estimation in deconvolution problems with unknown error distribution (2014)
  8. Montuelle, L.; Le Pennec, E.: Mixture of Gaussian regressions model with logistic weights, a penalized maximum likelihood approach (2014)
  9. Chagny, G.: Warped bases for conditional density estimation (2013)
  10. Fischer, Aurélie: Selecting the length of a principal curve within a Gaussian model (2013)
  11. Maugis-Rabusseau, C.; Michel, B.: Adaptive density estimation for clustering with Gaussian mixtures (2013)
  12. Oueslati, Abdullah; Lopez, Olivier: A proportional hazards regression model with change-points in the baseline function (2013)
  13. Saumard, Adrien: Optimal model selection in heteroscedastic regression using piecewise polynomial functions (2013)
  14. Bardet, Jean-Marc; Kengne, William; Wintenberger, Olivier: Multiple breaks detection in general causal time series using penalized quasi-likelihood (2012)
  15. Baudry, Jean-Patrick; Maugis, Cathy; Michel, Bertrand: Slope heuristics: overview and implementation (2012)
  16. Lerasle, Matthieu: Optimal model selection in density estimation (2012)
  17. Akakpo, Nathalie; Lacour, Claire: Inhomogeneous and anisotropic conditional density estimation from dependent data (2011)
  18. Caillerie, Claire; Michel, Bertrand: Model selection for simplicial approximation (2011)
  19. Fischer, Aurélie: On the number of groups in clustering (2011)
  20. Lerasle, Matthieu; Takahashi, Daniel Y.: An oracle approach for interaction neighborhood estimation in random fields (2011)