Linear Wavelet Density Estimation for Biased Data

To obtain L_p risk convergence rate, for a kind of density which has noise data, the linear wavelet estimator is constructed. In particular, when r≥p, the linear wavelets estimator is simple and the convergence rate is better than nonlinear estimator. In addition, when the bias function g(x) ≡1, the model is the case which has no noise, and the convergence rate is optimal and generalizes the result which was gotten.