Improved Nonparametric Density Estimation Using Additive Kernel Estimators

One way of improving the rate of convergent of classical kernel estimator is to use higher –order kernel function. In this thesis suggests anew” additive kernel estimator” to estimate f(x) , the proposed estimator are simple and interpretable as the higher –order estimator . The asymptotic properties of the proposed estimator are derived and formula for the smoothing parameter is given based on minimizing the asymptotic mean square error (AMSE), and some important case of this estimator are studied . Theoretical and practical result show the good potential properties of the proposed estimator over the higher –order kernel estimator .Keyword: Kernel method, higher –order kernel estimator, smoothing parameter, bias rate of convergence.