Wavelet Pointwise Estimation For A Class Of Density Function With Weight Function

Wavelet estimations have already received many significant achievements in density functions,medical statistics and econometrics.In this paper,we focus on the wavelet estimators of a class of density function with weight function to investigate their convergence in Holder space and give the upper bounds of their convergence order.Motivated by the work of Chaubey et al,(Y.P.Chaubey,C.Chesneau,H.Doosti.Adaptive wavelet estimation of a density from mixtures under multiplica-tive censoring.Statistics.2015,Vol.49,No.3,638-659),based on their linear and nonlinear wavelet estimators,we firstly study the convergence order of the linear estimator in Holder space,and give its upper bound.Since the linear estimator is related to the unknown space parameter s,it is non-adaptive and not applicable.Finally,we use the wavelet threshold method to explore the nonlinear wavelet esti-mator and obtain the same convergence order as the linear one up to a logarithmic factor.