Efron (1979) introduced the nonparametric tilting method, which enjoys many nice features, such as range-respecting, internal studentizing and good coverage accuracy. ^-1...[ Read more ]

Efron (1979) introduced the nonparametric tilting method, which enjoys many nice features, such as range-respecting, internal studentizing and good coverage accuracy.

In this thesis, the nonparametric tilting method is used in conjunction with the kernel method to construct confidence intervals based on a "mean-like" estimator in very general distributional contexts. Nonparametric tilting kernel density and regression estimators are given by using the tilting weights Pi instead of n^-1 in general bootstrap method. This nonparametric tilting method involves tilting the empirical distribution first, and then calculating the statistic under the tilted distribution. Furthermore, we have conducted some simulation studies to illustrate the performances for this method.