Local convergency rate of MSE in density estimation using the second-order modulus of smoothness

In this article, the local convergence rate of the mean square error (MSE) corresponding to a delta sequence-based density estimators is investigated by using second-order modulus of continuity type majorants. We look at the rate of convergency of the MSE of estimator for densities belonging to the class of functions which are defined by the second-order finite differences. The main contribution of this study is to obtain stronger convergence rate of a MSE by relaxing the second-order differentiation condition when compared with the class of density functions defined by the first-order finite differences.