Fiducial inference under nonparametric situations

Abstract

The object of the paper is to provide recipes for various fiducial inferences on a parameter under nonparametric situations. First, the fiducial empirical distribution of a random variable was introduced under nonparametric situations. And its almost sure behavior was established. Then based on it, fiducial model and hence fiducial distribution of a parameter are obtained. Further fiducial intervals of parameters as functionals of the population were constructed. Some of their frequentist properties were investigated under some mild conditions. Besides, p-values of some test hypotheses and their asymptotical properties were also given. Three applications of above results and further results were provided. For the mean, simulations on its interval estimator and hypothesis testing were conducted and their results suggest that the fiducial method performs better than others considered here.