Title
Optimal Distribution - Free Confidence Bands for a CDF
Speaker
Jesse Frey, The Ohio State University
Abstract
Distribution-free confidence bands for the CDF are typically found through inversion of a distribution-free hypothesis test. We propose an alternative strategy in which the upper and lower bounds of the confidence band are chosen to minimize a weighted width criterion. We derive necessary and sufficient conditions for a confidence band to be optimal with respect to such a criterion, and we demonstrate that optimal bands are unique in most cases of practical interest. Much of this theory is based on the famous Brunn-Minkowski Theorem from the theory of convex bodies. We construct optimal confidence bands both for the case of simple random sampling and for the case in which the observations are independent order statistics. This latter case includes schemes such as ranked-set sampling and nomination sampling. Our confidence bands in the independent order statistics case condition on the observed sequence of order statistics, and the computation of coverage probabilities is made possible by a new algorithm that does not seem to have any competitors in the literature.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.
