Other Applications of Confidence Bands
Confidence bands arise whenever a statistical analysis focuses on estimating a function.
For example, confidence bands can be constructed around estimates of the empirical distribution function. Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods .
Confidence bands have also been devised for estimates of density functions, spectral density functions, quantile functions, scatterplot smooths, survival functions, and characteristic functions.
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—William, Earl Of Pitt (1708–1778)
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—Bible: New Testament, Luke 2:6,7.