When the distribution of the estimator has the same shape for all values of the parameter, the distribution over the estimator can be used as a stand-in for the distribution over the true value.
Something you can use in place of something else because it's close enough for practical purposes—like using a sample of 1,000 people's opinions to represent what all Americans think.
To explain the fiducial argument we first set up a simple example. Say that we estimate the mean \(\theta\) of a normal distribution with unit variance over a variable \(X\). We collect a sample \(s\) consisting of measurements \(X_{1}, X_{2}, \ldots X_{n}\). The maximum likelihood estimator for \(\theta\) is the average value of the \(X_{i}\), that is, \(\hat{\theta}(s) = \sum_{i} X_{i} / n\). Under an assumed true value \(\theta\) we then have a normal distribution for the estimator \(\hat{\