Wavelet Pointwise Estimation For The Derivatives Of A Density Based On Biased Data

Density estimation is an important research direction of nonparametric statistical estimation,which plays a key role in signal processing,biology,medicine,economy and etc.A measured data usually contains noises,one of which is multiplication noise.On the other hand,many achievements have been made for estimation of the global errors.The study of local errors is relatively less,but sometimes more important.This thesis studies wavelet estimation for density derivatives under some multiplicative noises.More precisely,we will give upper bound estimates of a pointwise convergence rate for wavelet estimators in a Holder space.Motivated by the work of Chaubey et al(Y.P.Chaubey,E.Shirazi.On wavelet estimation of the derivatives of a density based on biased data.Communications in Statistics-Theory and Methods.2015,44:4491-4506),we firstly give an upper bound estimate of the pointwise convergence rate for a linear wavelet estimator.Then a non-linear wavelet estimator is considered in order to obtain the adaptivity.It attains the same convergence rate as that of the linear wavelet estimator up to a Inn factor.Fi-nally,numerical experiments are provided to compare our wavelet estimation with the classical kernel one.It turns out that the wavelet estimator performs better for some density functions.