Intrinsic Estimation

In this paper the problem of parametric point estimation is addressed from an objective Bayesian viewpoint. Arguing that pure statistical estimation may be appropriately described as a precise decision problem where the loss function is a measure of the divergence between the assumed model and the estimated model, the information-based intrinsic discrepancy is proposed as an appropriate loss function. The intrinsic estimator is then defined as that minimizing the expected loss with respect to the reference posterior distribution. The resulting estimators are shown have attractive invariance properties. As demonstrated with illustrative examples, the proposed theory either leads to new, arguably better estimators, or provides a new perspective on well-established solutions.