On a new higher order kernel for density estimation

Abstract

Higher order kernels have been widely implemented for nonparametric function estimation, mainly due to their faster asymptotic rates of convergence and interpretability. This article constructs a novel higher order kernel of any pre‐specified even order by using Shannon's formula. The proposed kernels have a closed form expression and are easy to implement. We compare the constructed kernel with several popular higher order kernels in the context of density estimation. Further, we observe that the mean integrated squared error (MISE) of the density estimator corresponding to the proposed kernel is comparable with that of the popular kernels. The constructed kernel performs somewhat better for the Fejér‐de la Vallée Poussin and the ‐symmetric densities. The MISE of the corresponding kernel density estimator and a few related theoretical results are also presented.