Wavelet linear estimation of a density and its derivatives from observations of mixtures under quadrant dependence

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

The estimation of a density and its derivatives from a finite mixture under the pairwise positive quadrant dependence assumption is considered. A new wavelet based linear estimator is constructed. We evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error. We prove that it attains a sharp rate of convergence for a wide class of unknown densities.

Mots clés: Density estimation; Mixtures; Quadrant dependence; Besov balls; Wavelets

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

Christophe Chesneau. Wavelet linear estimation of a density and its derivatives from observations of mixtures under quadrant dependence. 2011. ⟨hal-00510690v4⟩