Model selection for the segmentation of multiparameter exponential family distributions

Alice Cleynen (1) , Emilie Lebarbier (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 MIA-Paris - Mathématiques et Informatique Appliquées

We consider the segmentation problem of univariate distributions from the exponential family with multiple parameters. In segmenta-tion, the choice of the number of segments remains a difficult issue due to the discrete nature of the change-points. In this general exponential family distribution framework, we propose a penalized log-likelihood esti-mator where the penalty is inspired by papers of L. Birgé and P. Massart. The resulting estimator is proved to satisfy some oracle inequalities. We then further study the particular case of categorical variables by comparing the values of the key constants when derived from the specification of our general approach and when obtained by working directly with the characteristics of this distribution. Finally, simulation studies are conducted to assess the performance of our criterion and to compare our approach to other existing methods, and an application on real data modeled using the categorical distribution is provided.

Mots clés: model selection; Exponential family; distribution estimation; change-point detection

Domaines: Théorie [stat.TH]

Alice Cleynen, Emilie Lebarbier. Model selection for the segmentation of multiparameter exponential family distributions. Electronic Journal of Statistics , 2017, 11 (1), pp.800-842. ⟨10.1214/17-EJS1246⟩. ⟨hal-01590343⟩