Nonparametric confidence limits by resampling methods and least favorable families.

*(English)*Zbl 0715.62090Summary: The fundamental problem addressed in this paper is the problem of constructing confidence limits for a functional of a distribution in nonparametric settings. Specifically, given a random sample of observations from a distribution F, interest focuses on constructing confidence limits for a real valued functional \(\theta\) of F. Several procedures from the bootstrap literature are reviewed and, because no single method has emerged as the best solution for all problems, some new methods are presented as well. These new methods are motivated by an appropriate reduction of the nonparametric problem to a parametric problem with no nuisance parameters via the construction of a least favorable family. The coverage error of an approximate confidence limit is the difference between the exact coverage probability and the nominal level. All the procedures are compared by determining the exact order of coverage error of each method.

##### MSC:

62G15 | Nonparametric tolerance and confidence regions |

62G09 | Nonparametric statistical resampling methods |