A prior-free framework of coherent inference and its derivation of simple shrinkage estimators

While many coherent fiducial distributions coincide with confidence distributions or Bayesian posterior distributions, there is a general class of coherent fiducial distributions that equates the two-sided p-value with the probability that the null hypothesis is true. The use of that class leads to point estimators and interval estimators that can be derived neither from the dominant frequentist theory nor from Bayesian theories that rule out data-dependent priors. These simple estimators shrink toward the parameter value of the null hypothesis without relying on asymptotics or on prior distributions.