Some Remarks on Kernels

Kernel smoothing provides a simple way of finding a structure in data. Oneof the most popular settings where kernel smoothing ideas can be applied isthe simple regression model. In the context of kernel estimates of aregression function, the choice of a kernel from the different points ofview can be investigated. The aim of this paper is to present constructionsof minimum variance kernels and smooth kernels by means of the Legendrepolynomials and the Gegenbauer polynomials as well. Some of these kernelshave been introduced, e.g., in [2], [3], and [5], but here another approachby using the variational calculus is presented.