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. Bardet, Jean-Marc; Kamila, Kare; Kengne, William: Consistent model selection criteria and goodness-of-fit test for common time series models (2020)
  2. Bertin, Karine; Klutchnikoff, Nicolas; Léon, Jose R.; Prieur, Clémentine: Adaptive density estimation on bounded domains under mixing conditions (2020)
  3. Bock, Olivier; Collilieux, Xavier; Guillamon, François; Lebarbier, Emilie; Pascal, Claire: A breakpoint detection in the mean model with heterogeneous variance on fixed time intervals (2020)
  4. Alquier, Pierre; Doukhan, Paul; Fan, Xiequan: Exponential inequalities for nonstationary Markov chains (2019)
  5. Duval, Céline; Kappus, Johanna: Adaptive procedure for Fourier estimators: application to deconvolution and decompounding (2019)
  6. Ickowicz, Adrien; Ford, Jessica; Hayes, Keith: A mixture model approach for compositional data: inferring land-use influence on point-referenced water quality measurements (2019)
  7. Lehéricy, Luc: Consistent order estimation for nonparametric hidden Markov models (2019)
  8. Brault, Vincent; Ouadah, Sarah; Sansonnet, Laure; Lévy-Leduc, Céline: Nonparametric multiple change-point estimation for analyzing large Hi-C data matrices (2018)
  9. Comte, Fabienne; Samson, Adeline; Stirnemann, Julien J.: Hazard estimation with censoring and measurement error: application to length of pregnancy (2018)
  10. Comte, F.; Duval, C.: Statistical inference for renewal processes (2018)
  11. Devijver, Emilie; Gallopin, Mélina: Block-diagonal covariance selection for high-dimensional Gaussian graphical models (2018)
  12. Fop, Michael; Murphy, Thomas Brendan: Variable selection methods for model-based clustering (2018)
  13. Garreau, Damien; Arlot, Sylvain: Consistent change-point detection with kernels (2018)
  14. Gassiat, Elisabeth; Rousseau, Judith; Vernet, Elodie: Efficient semiparametric estimation and model selection for multidimensional mixtures (2018)
  15. Lehéricy, Luc: State-by-state minimax adaptive estimation for nonparametric hidden Markov models (2018)
  16. Li, Le; Guedj, Benjamin; Loustau, Sébastien: A quasi-Bayesian perspective to online clustering (2018)
  17. Chagny, G.; Comte, F.; Roche, A.: Adaptive estimation of the hazard rate with multiplicative censoring (2017)
  18. Devijver, Emilie: Model-based regression clustering for high-dimensional data: application to functional data (2017)
  19. Devijver, Emilie: Joint rank and variable selection for parsimonious estimation in a high-dimensional finite mixture regression model (2017)
  20. Lacour, Claire; Massart, Pascal; Rivoirard, Vincent: Estimator selection: a new method with applications to kernel density estimation (2017)

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