Wavelet Estimation For A Class Of Multiplicative Censored Models

In this paper,we use the wavelet method to study the Lp risk estimation for a density function in a multiplicative censored model.More precisely,we construct wave-let estimators,and show their consistency and convergence orders in the sense of Lp risk.Motivated by Yogendra P.Chaubey’s work(Yogendra P.Chaubey.Adaptive wave-let estimation of a density from mixtures under multiplicative censoring.Statistics.2015;49:3:638-659),we first prove the mean Lp consistency of the linear wavelet esti-mator without assuming any smoothness condition on a density function(it is assumed only to be in Lp);then the convergence order is provided for the linear estimators,when a density function belongs to a Besov space.It turns out that our result generalizes Chaubey’s theorem.Because the linear estimator is non-adaptive,we finally use the thresholding method to construct a nonlinear wavelet estimator,and give a convergence order of LP(1 ≤ p<∞)risk in a Besov space.