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

We consider the estimation of the location parameter θ 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, interpreted as the ‘population t-ratio.’ We show that the finite-sample distribution of these estimators is not centred at θ and is generally non-normal. In the asymptotic theory, we prove uniform n^(1/2)-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.