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Gaussian‐based kernels
Author(s) -
Wand Matthew P.,
Schucany William R.
Publication year - 1990
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315450
Subject(s) - mathematics , kernel (algebra) , smoothness , gaussian , computation , convolution (computer science) , extension (predicate logic) , polynomial , algorithm , fourier transform , gaussian function , mathematical optimization , computer science , mathematical analysis , discrete mathematics , artificial neural network , artificial intelligence , physics , quantum mechanics , programming language
We derive a class of higher‐order kernels for estimation of densities and their derivatives, which can be viewed as an extension of the second‐order Gaussian kernel. These kernels have some attractive properties such as smoothness, manageable convolution formulae, and Fourier transforms. One important application is the higher‐order extension of exact calculations of the mean integrated squared error. The proposed kernels also have the advantage of simplifying computations of common window‐width selection algorithms such as least‐squares cross‐validation. Efficiency calculations indicate that the Gaussian‐based kernels perform almost as well as the optimal polynomial kernels when die order of the derivative being estimated is low.