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 LMJL - Laboratoire de Mathématiques Jean Leray
4 University of Guelph

The estimation of a bi-dimensional density in the case of knowledge of the copula density is investigated. We propose a general estimator and study its performance under the mean integrated squared error (MISE). Then we derive an adaptive estimator based on wavelets. Under some smoothness assumptions, we show that it attains the standard unidimensional rate of convergence for a large class of unknown functions. We also report a short simulation study to support our theoretical findings.

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. 2014. ⟨hal-00979729v1⟩