Publication details

Kernel smoothing as a regularization of a singular distribution

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Authors

VESELÝ Vítězslav

Year of publication 1997
Type Article in Proceedings
Conference Proceedings of Summer Schools MATLAB 94, 95, Folia Fac. Sci. Nat. Univ. Masaryk. Brunensis, Mathematica 5
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords kernel smoothing; generalized functions; regularization
Description We approach the kernel smoothing method in a rather nontraditional manner, namely within the theory of generalized functions, completely avoiding the standard statistical reasoning. The kernel smoothing operation is considered as a process of finding a regular approximation (classical smooth function) to the given singular distribution (finite sequence of Dirac functions representing the non-smooth data). In particular the methods for construction of the commonly used kernel weight functions are investigated from this point of view, giving thus another insight into the basic ideas standing behind them.
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