Asymptotic effectiveness of two families of higher order kernels

Jones, M. C. and Wand, M. P. (1992). Asymptotic effectiveness of two families of higher order kernels. Journal of Statistical Planning and Inference, 31(1) pp. 15–21.

DOI: https://doi.org/10.1016/0378-3758(92)90038-T

Abstract

‘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 firstnamed families of kernels exhibit good theoretical performance for orders four and/or six, actually improving on the polynomial kernels for many such cases.

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