Global Efficiency

In this paper the global behavior of an estimator is studied in framework of Intrinsic Analysis, [1]. Two indices of performance of an estimator in a bounded region are analyzed: the average of the intrinsic risk (the loss function is the squared Rao distance) and the maximum risk. The Riemannian volume, provided by the Fisher metric on the manifold associated with the parametric model, allows us to take an average of the intrinsic risk. Cramér–Rao type integral inequalities for the integrated mean squared Rao distance of estimators are derived using variational methods, extending the previous work of several authors see, in particular, [2–5]. Additionally, lower bounds for the maximum risk are also derived, by using integral expressions.