Asymptotic Theory for Nonparametric Confidence Intervals
P. W. Glynn
Technical Report, Department of Operations Research, Stanford University (1982)
In practice, nonparametric confidence intervals often have undesirable small sample asymmetry and converge characteristics. By applying Edgeworth expansion theory, we obtain asymptotic expansions for the errors associated with nonparametric confidence intervals. This analysis isolates the various elements that contribute to error. We then proceed to develop first and second order corrections to the standard nonparametric interval, which deal with asymmetry problems and coverage difficulties, respectively.