A Comparative Study of Higher Order Kernel Estimation and Kernel Density Derivative Estimation of the Gaussian Kernel Estimator with Data Application

Higher-order kernel estimation and kernel density derivative estimation are techniques for reducing the asymptotic mean integrated squared error in nonparametric kernel density estimation. A reduction in the error criterion is an indication of better performance. The estimation of kernel function relies greatly on bandwidth and the identified reduction methods in the literature are bandwidths reliant for their implementation. This study examines the performance of higher order kernel estimation and kernel density derivatives estimation techniques with reference to the Gaussian kernel estimator owing to its wide applicability in real-life-settings. The explicit expressions for the bandwidth selectors of the two techniques in relation to the Gaussian kernel and the bandwidths were accurately obtained. Empirical results using two data sets obviously revealed that kernel density derivative estimation outperformed the higher order kernel estimation excellently well with the asymptotic mean integrated squared error as the criterion function.