On Asymptotic Properties of Generalized Fiducial Inference for Discretized Data

Abstract: Most data of which a statistician comes into contact has been rounded off in some manner, i.e., we do not observe X = x but a < X ≤ b. In this paper we investigate theoretical properties of the generalized fiducial distribution introduced in Hannig (2009) for such discretized data. Results are provided for both fixed sample size with increasing precision, and increasing sample size with fixed precision. In particular, we show that under very mild conditions the generalized fiducial distribution for i.i.d. discretized data will always lead to asymptotically correct inference. Resolution of several issues related to non-uniqueness of generalized fiducial distributions is also proposed.