On an intrinsic analysis of statistical estimation

摘要: Abstract In this paper we start considering the non-invariant under reparametrizations behaviour of some classical statistical estimation analysis tools, like bias and mean square error, trying to motivate convenience developing an intrinsic estimation. The Riemannian structure regular parametric models allows us, through notion centre mass, define measure, independently model parametrization. Some consequences are outlined, in particular relationship between unbiasedness a lower bound for Rao distance, invariant measure analogous version Rao-Blackwell theorem. Furthermore, using average distance as global performance estimator over certain region, it is possible obtain strictly positive bounds measure. other aspects also discussed.