Nonparametric Density Estimation in a Mixed Model Using Wavelets

This paper investigates nonparametric estimations of a density function within a mixed density model. A linear wavelet density estimator and an adaptive nonlinear wavelet estimator are proposed using wavelet method and hard thresholding algorithm. Under some mild conditions, the convergence rates over the mean integrated squared error of two wavelet density estimators are proved. Compared with the optimal convergence rates of nonparametric wavelet estimations, those two wavelet estimators all are optimal in some cases. Finally, the performances of two wavelet estimators are verified by numerical experimental studies.