Wavelet Estimation Of Density Derivatives For A Family Of Generalized Multiplicative Censoring Model

Multiplication censoring estimation is an important research direction for non-parametric statistics.Rao investigates the L2 risk estimation of density derivatives for a family of general-ized multiplication censoring model(B.L.S.Prakasa Rao.Wavelet estimation for derivative of a density in a GARCH-type model.Communications in Statistics Theory and Methods.2017,46:2396-2410).Motivated by the work of Rao,this thesis discusses the Lp(1?p ??)risk estimation of density derivatives for that model.Firstly,we provide the Lp(1 ?p ??)consistency of a linear wavelet estimator and show the upper bound estimation with Lp(1?p<?)risk over Besov spaces;Since the linear wavelet estimator is not adaptive,we give an upper bound estimation of Lp(1 ?p<?)risk for a nonlinear wavelet estimator over the same space;When p=2,our results reduce to the corresponding Rao 's theorems.Finally,a lower bound estimation is provided,which shows our upper bound estimations partially optimal,i.e.one of the upper bounds is optimal.