Abstract: In this paper we extend Fisher's fiducial argument and obtain a generalized fiducial recipe that greatly expands the applicability of fiducial ideas. We do this assuming as little structure as possible. We demonstrate this recipe on many examples of varying complexity. We investigate, by simulation and by theoretical considerations, some properties of the statistical procedures derived by the generalized fiducial recipe observing very good performance. We also compare the properties of generalized fiducial inference to the properties of Bayesian inference.
Key words and phrases: Asymptotics, fiducial inference, generalized inference, MCMC, mixture of normal distributions, multinomial distribution, structural inference.