Wavelet Pointwise Estimation Of Density Function For A Class Of Multiplicative Censoring Model

The density estimation of multiplicative censoring model is one of the research directions of nonparametric statistics,which has important applications in medical statistics,econometrics and other fields.Up to now,a lot of researches have focused on the global error estimation.But in many practical problems,local error is more concerned.In this thesis,we study the wavelet optimal estimation over the pointwise risk of a kind of multiplicative censoring model in the local Holder space.Firstly,we choose an appropriate wavelet basis to construct the linear wavelet estimator,and give the convergence order of the pointwise risk.Because of the non adaptivity of the linear wavelet estimation,we use the traditional method to discuss the nonlinear wavelet estimator.The result shows that it is adaptive and reaches the same convergence order as the linear one up to the factor ln n.In addition,since the nonlinear wavelet estimation depends on an unknown parameter's upper bound,this thesis also explores the data-driven estimator,which is entirely determined by the data and gives a better convergence rate than the nonlinear one.Finally,we show that all three types of estimators are optimal or nearly optimal(up to a logarithm factor).