Several criteria concerning the choice of kernels for the nonparametric estimation of functions and their derivatives are discussed. A specific optimality criterion is described which applies to kernels of compact support and of different orders of smoothness. The solutions of the corresponding variational problems are explicitly given. Many kernels discussed previously are obtained as special cases.
"Smooth Optimum Kernel Estimators of Densities, Regression Curves and Modes." Ann. Statist. 12 (2) 766 - 774, June, 1984. https://doi.org/10.1214/aos/1176346523