The mean consistency of wavelet estimators for convolutions of the density functions

In practical applications, people sometimes do not know whether the estimated function is smooth, and it is reasonable to consider the consistency of an estimator. Furthermore, the acquired data are usually contaminated by various random noises. In this paper, we develop the wavelet estimators for m-fold convolutions of the unknown density functions and consider their Lp(1≤p<∞) consistency under noiseless and additive noise situations, respectively. Finally, simulation studies illustrate the good performances of our nonparametric wavelet estimators.