Kernel smoothing as a regularization of a singular distribution
| Authors | |
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| 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 | |
| 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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