Abstract
In this paper we consider a generalization of the Fisher information measure, called the Fisher information of order s. We discuss some basic properties of this information measure, and show that it can be used to obtain bounds on the s-th absolute central moment of parameter estimators, for s ≥ 1. We give results for random parameters and for (nonrandom) location and scale parameters. The relation with other information measures is studied. Finally we give an application to parameter estimation in additive, nongaussian noise.
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