Bandwidth Selection for the Wolverton-Wagner Estimator

Fabienne Comte (1) , Nicolas Marie (2, 3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 MODAL'X - Modélisation aléatoire de Paris X
3 ESME - ESME - École spéciale de mécanique et d'électricité

For $n$ independent random variables having the same Hölder continuous density, this paper deals with controls of the Wolverton-Wagner's estimator MSE and MISE. Then, for a bandwidth $h_n(\beta)$, estimators of $\beta$ are obtained by a Goldenshluger-Lepski type method and a Lacour-Massart-Rivoirard type method. Some numerical experiments are provided for this last method.

Mots clés: Goldenshluger-Lepski method; Model selection; Density estimation; Lacour-Massart-Rivoirard method; Wolverton-Wagner estimator

Domaines: Statistiques [math.ST]

Fabienne Comte, Nicolas Marie. Bandwidth Selection for the Wolverton-Wagner Estimator. Journal of Statistical Planning and Inference, 2020, 207, pp.198-214. ⟨10.1016/j.jspi.2019.12.003⟩. ⟨hal-02004909v2⟩