Bayesian Estimation of the Normal Location Model: A Non‐Standard Approach

Abstract

We consider the estimation of the location parameter θ$$ \theta $$ in the normal location model and study the sampling properties of shrinkage estimators derived from a non‐standard Bayesian approach that places the prior on a scaled version of θ$$ \theta $$, interpreted as the “population t$$ t $$‐ratio.” We show that the finite‐sample distribution of these estimators is not centred at θ$$ \theta $$ and is generally non‐normal. In the asymptotic theory, we prove uniform n$$ \sqrt{n} $$‐consistency of our estimators and obtain their asymptotic distribution under a general moving‐parameter setup that includes both the fixed‐parameter and the local‐parameter settings as special cases.