CDF-based nonparametric confidence interval

In statistics, CDF-based nonparametric estimation is a general framework for generating confi- dence intervals around statistical functionals of a distribution. To use these methods, all that is required is a set of independently and identically distributed (iid) samples from the distribution and known bounds on the support of the distribution. The latter requirement simply means that all the nonzero probability mass of the distribution must be contained in some known interval [a, b].

Intuition

The intuition behind the CDF-based approach is that bounds on the CDF of a distribution can be translated into bounds on statistical functionals of that distribution. Given an upper and lower bound on the CDF, the approach involves finding the CDFs within the bounds that maximize and minimize the statistical functional of interest.