Improving the choice of higher order univariate kernels through bias reduction technique

Abstract

Within the last two decades, higher order univariate kernels have been under focus with respect to its importance in examining the concept of curve fitting. This paper has taken this direction by examining some basic properties of the univariate kernels in assessing and improving the choice of kernels. The minimum efficiency of the selected kernels is 82% at order 6. The global error diminishes as the order of h increases, and it is highest between orders 2 and 6, and beyond order 12 the global error seems to level off. Depending on the tolerance limit specified for the MISE and the percentage efficiency permitted, the extent of bias reduction required, can be monitored.