Fiducial approach to uncertainty assessment accounting for error due to instrument resolution

This paper presents an approach for making inference on the parameters μ and σ of a Gaussian distribution in the presence of resolution errors. The approach is based on the principle of fiducial inference and requires a Monte Carlo method for computing uncertainty intervals. A small simulation study is carried out to evaluate the performance of the proposed procedure and compare it with some of the existing procedures. The results indicate that the fiducial procedure is comparable to the best of the competing procedures for inference on μ. However, unlike some of the competing procedures, the same Monte Carlo calculations also provide inference for σ and many other related quantities of interest.