A note on the adaptive estimation of a bi-dimensional density in the case of knowledge of the copula density

Ingo Bulla (1) , Christophe Chesneau (2) , Fabien Navarro (3) , Tanya Mark (4)

1 LANL - Los Alamos National Laboratory
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme
3 Department of Mathematics and Statistics,Concordia University
4 University of Guelph

This paper attempts to better understand the influence of the smoothness of the copula density in the bi-dimensional estimation density problem. We provide an element of answer by studying the MISE properties of an adaptive estimator based on a plug-in approach and wavelet methods.

Mots clés: Density estimation; Wavelet methods; Copula density

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

Ingo Bulla, Christophe Chesneau, Fabien Navarro, Tanya Mark. A note on the adaptive estimation of a bi-dimensional density in the case of knowledge of the copula density. Statistics and Probability Letters, 2015, 105, ⟨10.1016/j.spl.2015.02.024⟩. ⟨hal-00979729v2⟩