EFFECTIVE INTERPOLATIONS FOR KERNEL DENSITY ESTIMATORS

In this paper we introduce a general interpolation scheme to be applie d in the kernel density estimation. Our scheme is based on a piecewise higher-degree polynomial interpolation with a strategically chosen se t of interpolation points. It is found that our interpolation scheme i mproves on the kernel density estimation in terms of the integrated me an squared error. A multivariate extension of our findings shows that the improvement increases substantially with the data dimension. In ad dition to the theoretical improvement, it is demonstrated that our int erpolation scheme brings about a considerable computational saving ove r the original kernel density estimator, making itself comparable to t he binning technique in the computational efficiency.