Adaptive wavelet estimation of a density from mixtures under multiplicative censoring

Yogendra P. Chaubey (1) , Christophe Chesneau (2) , Hassan Doosti (3)

1 Department of Mathematics and Statistics
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme
3 Department of Mathematics

In this paper, a mixture model under multiplicative censoring is considered. We investigate the estimation of a component of the mixture (a density) from the observations. A new adaptive estimator based on wavelets and a hard thresholding rule is constructed for this problem. Under mild assumptions on the model, we study its asymptotic properties by determining an upper bound of the mean integrated squared error over a wide range of Besov balls. We prove that the obtained upper bound is sharp.

Mots clés: Density estimation; mixture; Besov balls; wavelets; hard thresholding

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

Yogendra P. Chaubey, Christophe Chesneau, Hassan Doosti. Adaptive wavelet estimation of a density from mixtures under multiplicative censoring. 2013. ⟨hal-00918069⟩