Fisher Information and Spline Interpolation
The Annals of Statistics · 1974 · Volume 2 · Issue 5
Abstract
It is shown that among all cumulative distribution functions passing through $k \geqq 2$ given points there is a unique one with minimal Fisher information; it is obtained by a curious type of spline interpolation. This answers some questions raisd by D. G. Kendall and J. W. Tukey.
Keywords
41A15, 62G05, Fisher information, interpolation, nonparametric estimation, splines
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