HIGHER ORDER FORMS OF SOME ASYMMETRIC KERNELS

Abstract

This paper is to investigate the properties of higher-order form of some asymmetric kernels and consider its relevance to human life. The higher – order forms of some asymmetric kernels were derived from their asymmetric counterpart based on the formula by Jones and Foster (1993). The performances of these asymmetric kernels and their higher – order counterpart were considered in terms of their mean integrated squared error, asymptotic mean integrated squared error (AMISE) and their optimal window width h. The results of these asymmetric kernels and that of their higher – order asymmetric counterparts are compared. An appreciable error reduction was achieved in the higher-order asymmetric kernel when compared to their asymmetric counterparts. The error propagation also drops considerably as h increases. This method can be used to forecast performances of stock exchange and insurance claim.

Key words: asymmetric kernels, higher – order forms of asymmetric kernels, exponential and gamma kernels, asymptotic mean integrated squared error (AMISE) and the optimal window width.