A note about the critical bandwidth for a kernel density estimator with the uniform kernel

Raphaël Coudret (1, 2, 3) , Gilles Durrieu (4) , Jerome Saracco (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 EPOC - Environnements et Paléoenvironnements OCéaniques
4 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

Among available bandwidths for kernel density estimators, the critical bandwidth is a data-driven one, which satisfies a constraint on the number of modes of the estimated density. When using a random bandwidth, it is of particular interest to show that it goes toward 0 in probability when the sample size goes to infinity. Such a property is important to prove satisfying asymptotic results about the corresponding kernel density estimator. It is shown here that this property is not true for the uniform kernel.

Mots clés: Bandwidth; Kernel density estimator; Mode

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Raphaël Coudret, Gilles Durrieu, Jerome Saracco. A note about the critical bandwidth for a kernel density estimator with the uniform kernel. 2012. ⟨hal-00765843⟩