ASYMPTOTIC EFFECTIVENESS OF SOME HIGHER-ORDER KERNELS

'Spline-equivalent' kernels and 'exponential power' kernels are considered as higher order kernels for use in kernel estimation of a function and its derivatives. They form two more practicable classes of alternatives to 'optimal' polynomial kernels, along with Gaussian-based ones. Both first-named families of kernels exhibit good theoretical performance for orders four and/or six, actually improving on the polynomial kernels for many such cases.