The De Forest Iteration Problem.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Schoenbergs results on the limiting behavior of the normalized coefficients of the n-fold iterate of a symmetrical linear smoothing formula are extended to the unsymmetrical case. When the formula is exact to an odd degree, the family of limiting functions obtained is the same as that deduced by Schoenberg. When it is exact to an even degree possible only for an unsymmetrical formula, the limiting functions belong to a different family defined by very slowly converging Fourier integrals and including the Airy function as a particular case. A rebuttal is offered to a certain theoretical objection to even-degree smoothing formulae, and, as a curious by-product, a certain unsymmetrical 5-term formula exact to degree two is shown to be a better smoothing agent than the corresponding 5-term symmetrical formula. Author
- Statistics and Probability