De Luca, G., Magnus, JanR. and Peracchi, F. (2025). Bayesian Estimation of the Normal Location Model: A Non-Standard Approach Oxford Bulletin of Economics and Statistics, :.

We consider the estimation of the location parameter (Formula presented.) 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 (Formula presented.), interpreted as the “population (Formula presented.) -ratio.” We show that the finite-sample distribution of these estimators is not centred at (Formula presented.) and is generally non-normal. In the asymptotic theory, we prove uniform (Formula presented.) -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.