Some asymptotic results for fiducial and confidence distributions

Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations are accurate at least to order O(n−1). For the mean parameter μ=(μ1,…,μk) of an exponential family, our fiducial distribution is asymptotically normal and invariant to the importance ordering of the μi's.