Let be a random sample, its components are observations from a distribution-function . The empirical distribution function is a nonparametric maximum likelihood estimate of . maximizes
over all distribution functions F. Let be the empirical likelihood ratio function and T(.) any functional. It is shown that sets of the form
may be used as confidence regions for some like the sample mean or a class of M-estimators (especially the quantiles of . These confidence intervals are compared in a simulation study to some bootstrap confidence intervals and to confidence intervals based on a t-statistic for a confidence coefficient . It seems that two of the bootstrap intervals may be recommended but the simulation is based on 1000 runs only.