On Asymptotic Mean Integrated Squared Error’s Reduction Techniques in Kernel Density Estimation

Abstract

The techniques of asymptotic mean integrated squared error’s reduction in kernel density estimation is the focus of this paper. The asymptotic mean integrated squared error (AMISE) is an optimality criterion function that measures the performance of a kernel density estimator. This criterion function is made up of two components, and the contributions of both components to the AMISE are mainly regulated by the smoothing parameter. Kernel density estimation are of vitally importance in statistical data analysis especially for exploratory and visualization purposes. In performance evaluation, a method is better when it produces a smaller value of the AMISE; hence effort is being made to develop techniques that reduce the AMISE while ensuring that in practical implementation using real data, the statistical properties of the given observations are retained. We consider the kernel density derivative and kernel boosting as the AMISE reduction techniques. In kernel boosting, we introduce the optimal smoothing parameter selector for each boosting steps as the number of iteration increases. The presented results show that the AMISE decreases with higher kernel derivatives and also as the number of boosting steps increases.